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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 id = "l00001" name = "l00001" > < / a > < span class = "lineno" > 1< / span > < span class = "comment" > // Copyright 2010-2021 Google LLC< / span > < / div >
< div class = "line" > < a id = "l00002" name = "l00002" > < / a > < span class = "lineno" > 2< / span > < span class = "comment" > // Licensed under the Apache License, Version 2.0 (the " License" );< / span > < / div >
< div class = "line" > < a id = "l00003" 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 >
< div class = "line" > < a id = "l00004" name = "l00004" > < / a > < span class = "lineno" > 4< / span > < span class = "comment" > // You may obtain a copy of the License at< / span > < / div >
< div class = "line" > < a id = "l00005" name = "l00005" > < / a > < span class = "lineno" > 5< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00006" name = "l00006" > < / a > < span class = "lineno" > 6< / span > < span class = "comment" > // http://www.apache.org/licenses/LICENSE-2.0< / span > < / div >
< div class = "line" > < a id = "l00007" name = "l00007" > < / a > < span class = "lineno" > 7< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00008" name = "l00008" > < / a > < span class = "lineno" > 8< / span > < span class = "comment" > // Unless required by applicable law or agreed to in writing, software< / span > < / div >
< div class = "line" > < a id = "l00009" name = "l00009" > < / a > < span class = "lineno" > 9< / span > < span class = "comment" > // distributed under the License is distributed on an " AS IS" BASIS,< / span > < / div >
< div class = "line" > < a id = "l00010" name = "l00010" > < / a > < span class = "lineno" > 10< / span > < span class = "comment" > // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.< / span > < / div >
< div class = "line" > < a id = "l00011" name = "l00011" > < / a > < span class = "lineno" > 11< / span > < span class = "comment" > // See the License for the specific language governing permissions and< / span > < / div >
< div class = "line" > < a id = "l00012" name = "l00012" > < / a > < span class = "lineno" > 12< / span > < span class = "comment" > // limitations under the License.< / span > < / div >
< div class = "line" > < a id = "l00013" name = "l00013" > < / a > < span class = "lineno" > 13< / span > < / div >
< div class = "line" > < a id = "l00014" name = "l00014" > < / a > < span class = "lineno" > 14< / span > < span class = "preprocessor" > #ifndef OR_TOOLS_UTIL_SATURATED_ARITHMETIC_H_< / span > < / div >
< div class = "line" > < a id = "l00015" name = "l00015" > < / a > < span class = "lineno" > 15< / span > < span class = "preprocessor" > #define OR_TOOLS_UTIL_SATURATED_ARITHMETIC_H_< / span > < / div >
< div class = "line" > < a id = "l00016" name = "l00016" > < / a > < span class = "lineno" > 16< / span > < / div >
< div class = "line" > < a id = "l00017" name = "l00017" > < / a > < span class = "lineno" > 17< / span > < span class = "preprocessor" > #include " absl/base/casts.h" < / span > < / div >
< div class = "line" > < a id = "l00018" 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 >
< div class = "line" > < a id = "l00019" 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 >
< div class = "line" > < a id = "l00020" name = "l00020" > < / a > < span class = "lineno" > 20< / span > < / div >
< div class = "line" > < a id = "l00021" name = "l00021" > < / a > < span class = "lineno" > 21< / span > < span class = "keyword" > namespace < / span > < a class = "code hl_namespace" href = "namespaceoperations__research.html" > operations_research< / a > {< / div >
< div class = "line" > < a id = "l00022" name = "l00022" > < / a > < span class = "lineno" > 22< / span > < span class = "comment" > // ---------- Overflow utility functions ----------< / span > < / div >
< div class = "line" > < a id = "l00023" name = "l00023" > < / a > < span class = "lineno" > 23< / span > < / div >
< div class = "line" > < a id = "l00024" name = "l00024" > < / a > < span class = "lineno" > 24< / span > < span class = "comment" > // Implement two' s complement addition and subtraction on int64s.< / span > < / div >
< div class = "line" > < a id = "l00025" name = "l00025" > < / a > < span class = "lineno" > 25< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00026" 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 >
< div class = "line" > < a id = "l00027" name = "l00027" > < / a > < span class = "lineno" > 27< / span > < span class = "comment" > // undefined. This is because of the different possible representations that may< / span > < / div >
< div class = "line" > < a id = "l00028" 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 >
< div class = "line" > < a id = "l00029" name = "l00029" > < / a > < span class = "lineno" > 29< / span > < span class = "comment" > // magnitude). Such overflows are detected by Address Sanitizer with< / span > < / div >
< div class = "line" > < a id = "l00030" name = "l00030" > < / a > < span class = "lineno" > 30< / span > < span class = "comment" > // -fsanitize=signed-integer-overflow.< / span > < / div >
< div class = "line" > < a id = "l00031" name = "l00031" > < / a > < span class = "lineno" > 31< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00032" name = "l00032" > < / a > < span class = "lineno" > 32< / span > < span class = "comment" > // Simple, portable overflow detection on current machines relies on< / span > < / div >
< div class = "line" > < a id = "l00033" 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 >
< div class = "line" > < a id = "l00034" name = "l00034" > < / a > < span class = "lineno" > 34< / span > < span class = "comment" > // integers is negative, there has been an overflow.< / span > < / div >
< div class = "line" > < a id = "l00035" name = "l00035" > < / a > < span class = "lineno" > 35< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00036" 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 >
< div class = "line" > < a id = "l00037" name = "l00037" > < / a > < span class = "lineno" > 37< / span > < span class = "comment" > // which do not use two' s complement.< / span > < / div >
< div class = "line" > < a id = "l00038" name = "l00038" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a2e03c61d96b37a3533c3ffcec93fc18d" > 38< / a > < / span > < span class = "keyword" > inline< / span > int64_t < a class = "code hl_function" href = "namespaceoperations__research.html#a2e03c61d96b37a3533c3ffcec93fc18d" > TwosComplementAddition< / a > (int64_t x, int64_t y) {< / div >
< div class = "line" > < a id = "l00039" name = "l00039" > < / a > < span class = "lineno" > 39< / span > < span class = "keyword" > static_assert< / span > (< span class = "keyword" > static_cast< < / span > uint64_t< span class = "keyword" > > < / span > (-1LL) == ~0ULL,< / div >
< div class = "line" > < a id = "l00040" name = "l00040" > < / a > < span class = "lineno" > 40< / span > < span class = "stringliteral" > " The target architecture does not use two' s complement." < / span > );< / div >
< div class = "line" > < a id = "l00041" name = "l00041" > < / a > < span class = "lineno" > 41< / span > < span class = "keywordflow" > return< / span > absl::bit_cast< int64_t> (< span class = "keyword" > static_cast< < / span > uint64_t< span class = "keyword" > > < / span > (x) +< / div >
< div class = "line" > < a id = "l00042" name = "l00042" > < / a > < span class = "lineno" > 42< / span > < span class = "keyword" > static_cast< < / span > uint64_t< span class = "keyword" > > < / span > (y));< / div >
< div class = "line" > < a id = "l00043" name = "l00043" > < / a > < span class = "lineno" > 43< / span > }< / div >
< div class = "line" > < a id = "l00044" name = "l00044" > < / a > < span class = "lineno" > 44< / span > < / div >
< div class = "line" > < a id = "l00045" name = "l00045" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#ab7f89c34e63aca5f186808225f45865b" > 45< / a > < / span > < span class = "keyword" > inline< / span > int64_t < a class = "code hl_function" href = "namespaceoperations__research.html#ab7f89c34e63aca5f186808225f45865b" > TwosComplementSubtraction< / a > (int64_t x, int64_t y) {< / div >
< div class = "line" > < a id = "l00046" name = "l00046" > < / a > < span class = "lineno" > 46< / span > < span class = "keyword" > static_assert< / span > (< span class = "keyword" > static_cast< < / span > uint64_t< span class = "keyword" > > < / span > (-1LL) == ~0ULL,< / div >
< div class = "line" > < a id = "l00047" name = "l00047" > < / a > < span class = "lineno" > 47< / span > < span class = "stringliteral" > " The target architecture does not use two' s complement." < / span > );< / div >
< div class = "line" > < a id = "l00048" name = "l00048" > < / a > < span class = "lineno" > 48< / span > < span class = "keywordflow" > return< / span > absl::bit_cast< int64_t> (< span class = "keyword" > static_cast< < / span > uint64_t< span class = "keyword" > > < / span > (x) -< / div >
< div class = "line" > < a id = "l00049" name = "l00049" > < / a > < span class = "lineno" > 49< / span > < span class = "keyword" > static_cast< < / span > uint64_t< span class = "keyword" > > < / span > (y));< / div >
< div class = "line" > < a id = "l00050" name = "l00050" > < / a > < span class = "lineno" > 50< / span > }< / div >
< div class = "line" > < a id = "l00051" name = "l00051" > < / a > < span class = "lineno" > 51< / span > < / div >
< div class = "line" > < a id = "l00052" name = "l00052" > < / a > < span class = "lineno" > 52< / span > < span class = "comment" > // Helper function that returns true if an overflow has occurred in computing< / span > < / div >
< div class = "line" > < a id = "l00053" name = "l00053" > < / a > < span class = "lineno" > 53< / span > < span class = "comment" > // sum = x + y. sum is expected to be computed elsewhere.< / span > < / div >
< div class = "line" > < a id = "l00054" name = "l00054" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a0d130d7d0baf49b66a6938714828d0aa" > 54< / a > < / span > < span class = "keyword" > inline< / span > < span class = "keywordtype" > bool< / span > < a class = "code hl_function" href = "namespaceoperations__research.html#a0d130d7d0baf49b66a6938714828d0aa" > AddHadOverflow< / a > (int64_t x, int64_t y, int64_t sum) {< / div >
< div class = "line" > < a id = "l00055" name = "l00055" > < / a > < span class = "lineno" > 55< / span > < span class = "comment" > // Overflow cannot occur if operands have different signs.< / span > < / div >
< div class = "line" > < a id = "l00056" name = "l00056" > < / a > < span class = "lineno" > 56< / span > < span class = "comment" > // It can only occur if sign(x) == sign(y) and sign(sum) != sign(x),< / span > < / div >
< div class = "line" > < a id = "l00057" name = "l00057" > < / a > < span class = "lineno" > 57< / span > < span class = "comment" > // which is equivalent to: sign(x) != sign(sum) & & sign(y) != sign(sum).< / span > < / div >
< div class = "line" > < a id = "l00058" name = "l00058" > < / a > < span class = "lineno" > 58< / span > < span class = "comment" > // This is captured when the expression below is negative.< / span > < / div >
< div class = "line" > < a id = "l00059" name = "l00059" > < / a > < span class = "lineno" > 59< / span > < a class = "code hl_define" href = "base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0" > DCHECK_EQ< / a > (sum, < a class = "code hl_function" href = "namespaceoperations__research.html#a2e03c61d96b37a3533c3ffcec93fc18d" > TwosComplementAddition< / a > (x, y));< / div >
< div class = "line" > < a id = "l00060" name = "l00060" > < / a > < span class = "lineno" > 60< / span > < span class = "keywordflow" > return< / span > ((x ^ sum) & (y ^ sum)) < 0;< / div >
< div class = "line" > < a id = "l00061" name = "l00061" > < / a > < span class = "lineno" > 61< / span > }< / div >
< div class = "line" > < a id = "l00062" name = "l00062" > < / a > < span class = "lineno" > 62< / span > < / div >
< div class = "line" > < a id = "l00063" name = "l00063" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#ab5b3d385e40264b5c3094b64d10a2299" > 63< / a > < / span > < span class = "keyword" > inline< / span > < span class = "keywordtype" > bool< / span > < a class = "code hl_function" href = "namespaceoperations__research.html#ab5b3d385e40264b5c3094b64d10a2299" > SubHadOverflow< / a > (int64_t x, int64_t y, int64_t diff) {< / div >
< div class = "line" > < a id = "l00064" name = "l00064" > < / a > < span class = "lineno" > 64< / span > < span class = "comment" > // This is the same reasoning as for AddHadOverflow. We have x = diff + y.< / span > < / div >
< div class = "line" > < a id = "l00065" name = "l00065" > < / a > < span class = "lineno" > 65< / span > < span class = "comment" > // The formula is the same, with ' x' and diff exchanged.< / span > < / div >
< div class = "line" > < a id = "l00066" name = "l00066" > < / a > < span class = "lineno" > 66< / span > < a class = "code hl_define" href = "base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0" > DCHECK_EQ< / a > (diff, < a class = "code hl_function" href = "namespaceoperations__research.html#ab7f89c34e63aca5f186808225f45865b" > TwosComplementSubtraction< / a > (x, y));< / div >
< div class = "line" > < a id = "l00067" name = "l00067" > < / a > < span class = "lineno" > 67< / span > < span class = "keywordflow" > return< / span > < a class = "code hl_function" href = "namespaceoperations__research.html#a0d130d7d0baf49b66a6938714828d0aa" > AddHadOverflow< / a > (diff, y, x);< / div >
< div class = "line" > < a id = "l00068" name = "l00068" > < / a > < span class = "lineno" > 68< / span > }< / div >
< div class = "line" > < a id = "l00069" name = "l00069" > < / a > < span class = "lineno" > 69< / span > < / div >
< div class = "line" > < a id = "l00070" name = "l00070" > < / a > < span class = "lineno" > 70< / span > < span class = "comment" > // A note on overflow treatment.< / span > < / div >
< div class = "line" > < a id = "l00071" name = "l00071" > < / a > < span class = "lineno" > 71< / span > < span class = "comment" > // kint64min and kint64max are treated as infinity.< / span > < / div >
< div class = "line" > < a id = "l00072" name = "l00072" > < / a > < span class = "lineno" > 72< / span > < span class = "comment" > // Thus if the computation overflows, the result is always kint64m(ax/in).< / span > < / div >
< div class = "line" > < a id = "l00073" name = "l00073" > < / a > < span class = "lineno" > 73< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00074" name = "l00074" > < / a > < span class = "lineno" > 74< / span > < span class = "comment" > // Note(user): this is actually wrong: when computing A-B, if A is kint64max< / span > < / div >
< div class = "line" > < a id = "l00075" name = "l00075" > < / a > < span class = "lineno" > 75< / span > < span class = "comment" > // and B is finite, then A-B won' t be kint64max: overflows aren' t sticky.< / span > < / div >
< div class = "line" > < a id = "l00076" name = "l00076" > < / a > < span class = "lineno" > 76< / span > < span class = "comment" > // TODO(user): consider making some operations overflow-sticky, some others< / span > < / div >
< div class = "line" > < a id = "l00077" name = "l00077" > < / a > < span class = "lineno" > 77< / span > < span class = "comment" > // not, but make an explicit choice throughout.< / span > < / div >
< div class = "line" > < a id = "l00078" name = "l00078" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a93bd93f028c18a4b55b30056ef60df44" > 78< / a > < / span > < span class = "keyword" > inline< / span > < span class = "keywordtype" > bool< / span > < a class = "code hl_function" href = "namespaceoperations__research.html#a93bd93f028c18a4b55b30056ef60df44" > AddOverflows< / a > (int64_t x, int64_t y) {< / div >
< div class = "line" > < a id = "l00079" name = "l00079" > < / a > < span class = "lineno" > 79< / span > < span class = "keywordflow" > return< / span > < a class = "code hl_function" href = "namespaceoperations__research.html#a0d130d7d0baf49b66a6938714828d0aa" > AddHadOverflow< / a > (x, y, < a class = "code hl_function" href = "namespaceoperations__research.html#a2e03c61d96b37a3533c3ffcec93fc18d" > TwosComplementAddition< / a > (x, y));< / div >
< div class = "line" > < a id = "l00080" name = "l00080" > < / a > < span class = "lineno" > 80< / span > }< / div >
< div class = "line" > < a id = "l00081" name = "l00081" > < / a > < span class = "lineno" > 81< / span > < / div >
< div class = "line" > < a id = "l00082" name = "l00082" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a0004fd13375ee41f234051cb5cc74869" > 82< / a > < / span > < span class = "keyword" > inline< / span > int64_t < a class = "code hl_function" href = "namespaceoperations__research.html#a0004fd13375ee41f234051cb5cc74869" > SubOverflows< / a > (int64_t x, int64_t y) {< / div >
< div class = "line" > < a id = "l00083" name = "l00083" > < / a > < span class = "lineno" > 83< / span > < span class = "keywordflow" > return< / span > < a class = "code hl_function" href = "namespaceoperations__research.html#ab5b3d385e40264b5c3094b64d10a2299" > SubHadOverflow< / a > (x, y, < a class = "code hl_function" href = "namespaceoperations__research.html#ab7f89c34e63aca5f186808225f45865b" > TwosComplementSubtraction< / a > (x, y));< / div >
< div class = "line" > < a id = "l00084" name = "l00084" > < / a > < span class = "lineno" > 84< / span > }< / div >
< div class = "line" > < a id = "l00085" name = "l00085" > < / a > < span class = "lineno" > 85< / span > < / div >
< div class = "line" > < a id = "l00086" name = "l00086" > < / a > < span class = "lineno" > 86< / span > < span class = "comment" > // Performs *b += a and returns false iff the addition overflow or underflow.< / span > < / div >
< div class = "line" > < a id = "l00087" name = "l00087" > < / a > < span class = "lineno" > 87< / span > < span class = "comment" > // This function only works for typed integer type (IntType< > ).< / span > < / div >
< div class = "line" > < a id = "l00088" name = "l00088" > < / a > < span class = "lineno" > 88< / span > < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > IntegerType> < / div >
< div class = "line" > < a id = "l00089" name = "l00089" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#ae1bd0133149b70b678b123524541aaad" > 89< / a > < / span > < span class = "keywordtype" > bool< / span > < a class = "code hl_function" href = "namespaceoperations__research.html#ae1bd0133149b70b678b123524541aaad" > SafeAddInto< / a > (IntegerType < a class = "code hl_variable" href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > , IntegerType* < a class = "code hl_variable" href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > ) {< / div >
< div class = "line" > < a id = "l00090" name = "l00090" > < / a > < span class = "lineno" > 90< / span > < span class = "keyword" > const< / span > int64_t x = < a class = "code hl_variable" href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > .value();< / div >
< div class = "line" > < a id = "l00091" name = "l00091" > < / a > < span class = "lineno" > 91< / span > < span class = "keyword" > const< / span > int64_t y = < a class = "code hl_variable" href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > -> value();< / div >
< div class = "line" > < a id = "l00092" name = "l00092" > < / a > < span class = "lineno" > 92< / span > < span class = "keyword" > const< / span > int64_t sum = < a class = "code hl_function" href = "namespaceoperations__research.html#a2e03c61d96b37a3533c3ffcec93fc18d" > TwosComplementAddition< / a > (x, y);< / div >
< div class = "line" > < a id = "l00093" name = "l00093" > < / a > < span class = "lineno" > 93< / span > < span class = "keywordflow" > if< / span > (< a class = "code hl_function" href = "namespaceoperations__research.html#a0d130d7d0baf49b66a6938714828d0aa" > AddHadOverflow< / a > (x, y, sum)) < span class = "keywordflow" > return< / span > < span class = "keyword" > false< / span > ;< / div >
< div class = "line" > < a id = "l00094" name = "l00094" > < / a > < span class = "lineno" > 94< / span > *< a class = "code hl_variable" href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > = sum;< / div >
< div class = "line" > < a id = "l00095" name = "l00095" > < / a > < span class = "lineno" > 95< / span > < span class = "keywordflow" > return< / span > < span class = "keyword" > true< / span > ;< / div >
< div class = "line" > < a id = "l00096" name = "l00096" > < / a > < span class = "lineno" > 96< / span > }< / div >
< div class = "line" > < a id = "l00097" name = "l00097" > < / a > < span class = "lineno" > 97< / span > < / div >
< div class = "line" > < a id = "l00098" name = "l00098" > < / a > < span class = "lineno" > 98< / span > < span class = "comment" > // Returns kint64max if x > = 0 and kint64min if x < 0.< / span > < / div >
< div class = "line" > < a id = "l00099" name = "l00099" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a28f4f86e4cc6cfc5e075577baabd00f2" > 99< / a > < / span > < span class = "keyword" > inline< / span > int64_t < a class = "code hl_function" href = "namespaceoperations__research.html#a28f4f86e4cc6cfc5e075577baabd00f2" > CapWithSignOf< / a > (int64_t x) {< / div >
< div class = "line" > < a id = "l00100" name = "l00100" > < / a > < span class = "lineno" > 100< / span > < span class = "comment" > // return kint64max if x > = 0 or kint64max + 1 (== kint64min) if x < 0.< / span > < / div >
< div class = "line" > < a id = "l00101" name = "l00101" > < / a > < span class = "lineno" > 101< / span > < span class = "keywordflow" > return< / span > < a class = "code hl_function" href = "namespaceoperations__research.html#a2e03c61d96b37a3533c3ffcec93fc18d" > TwosComplementAddition< / a > (< a class = "code hl_variable" href = "integral__types_8h.html#a808bd435380aa1e2bbd6f13ac7759897" > kint64max< / a > , < span class = "keyword" > static_cast< < / span > int64_t< span class = "keyword" > > < / span > (x < 0));< / div >
< div class = "line" > < a id = "l00102" name = "l00102" > < / a > < span class = "lineno" > 102< / span > }< / div >
< div class = "line" > < a id = "l00103" name = "l00103" > < / a > < span class = "lineno" > 103< / span > < / div >
< div class = "line" > < a id = "l00104" name = "l00104" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a92790ebe58f31601890072ac2d4911c5" > 104< / a > < / span > < span class = "keyword" > inline< / span > int64_t < a class = "code hl_function" href = "namespaceoperations__research.html#a92790ebe58f31601890072ac2d4911c5" > CapAddGeneric< / a > (int64_t x, int64_t y) {< / div >
< div class = "line" > < a id = "l00105" name = "l00105" > < / a > < span class = "lineno" > 105< / span > < span class = "keyword" > const< / span > int64_t result = < a class = "code hl_function" href = "namespaceoperations__research.html#a2e03c61d96b37a3533c3ffcec93fc18d" > TwosComplementAddition< / a > (x, y);< / div >
< div class = "line" > < a id = "l00106" name = "l00106" > < / a > < span class = "lineno" > 106< / span > < span class = "keywordflow" > return< / span > < a class = "code hl_function" href = "namespaceoperations__research.html#a0d130d7d0baf49b66a6938714828d0aa" > AddHadOverflow< / a > (x, y, result) ? < a class = "code hl_function" href = "namespaceoperations__research.html#a28f4f86e4cc6cfc5e075577baabd00f2" > CapWithSignOf< / a > (x) : result;< / div >
< div class = "line" > < a id = "l00107" name = "l00107" > < / a > < span class = "lineno" > 107< / span > }< / div >
< div class = "line" > < a id = "l00108" name = "l00108" > < / a > < span class = "lineno" > 108< / span > < / div >
< div class = "line" > < a id = "l00109" name = "l00109" > < / a > < span class = "lineno" > 109< / span > < span class = "preprocessor" > #if defined(__GNUC__) & & defined(__x86_64__)< / span > < / div >
< div class = "line" > < a id = "l00110" name = "l00110" > < / a > < span class = "lineno" > 110< / span > < span class = "comment" > // TODO(user): port this to other architectures.< / span > < / div >
< div class = "line" > < a id = "l00111" name = "l00111" > < / a > < span class = "lineno" > 111< / span > < span class = "keyword" > inline< / span > int64_t CapAddFast(int64_t x, int64_t y) {< / div >
< div class = "line" > < a id = "l00112" name = "l00112" > < / a > < span class = "lineno" > 112< / span > < span class = "keyword" > const< / span > int64_t cap = < a class = "code hl_function" href = "namespaceoperations__research.html#a28f4f86e4cc6cfc5e075577baabd00f2" > CapWithSignOf< / a > (x);< / div >
< div class = "line" > < a id = "l00113" name = "l00113" > < / a > < span class = "lineno" > 113< / span > int64_t result = x;< / div >
< div class = "line" > < a id = "l00114" name = "l00114" > < / a > < span class = "lineno" > 114< / span > < span class = "comment" > // clang-format off< / span > < / div >
< div class = "line" > < a id = "l00115" name = "l00115" > < / a > < span class = "lineno" > 115< / span > < span class = "keyword" > asm< / span > < span class = "keyword" > volatile< / span > ( < span class = "comment" > // ' volatile' : ask compiler optimizer " keep as is" .< / span > < / div >
< div class = "line" > < a id = "l00116" name = "l00116" > < / a > < span class = "lineno" > 116< / span > < span class = "stringliteral" > " \t" < / span > < span class = "stringliteral" > " addq %[y],%[result]" < / span > < / div >
< div class = "line" > < a id = "l00117" name = "l00117" > < / a > < span class = "lineno" > 117< / span > < span class = "stringliteral" > " \n\t" < / span > < span class = "stringliteral" > " cmovoq %[cap],%[result]" < / span > < span class = "comment" > // Conditional move if overflow.< / span > < / div >
< div class = "line" > < a id = "l00118" name = "l00118" > < / a > < span class = "lineno" > 118< / span > : [result] < span class = "stringliteral" > " =r" < / span > (result) < span class = "comment" > // Output< / span > < / div >
< div class = "line" > < a id = "l00119" name = "l00119" > < / a > < span class = "lineno" > 119< / 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 >
< div class = "line" > < a id = "l00120" name = "l00120" > < / a > < span class = "lineno" > 120< / span > : < span class = "stringliteral" > " cc" < / span > < span class = "comment" > /* Clobbered registers */< / span > );< / div >
< div class = "line" > < a id = "l00121" name = "l00121" > < / a > < span class = "lineno" > 121< / span > < span class = "comment" > // clang-format on< / span > < / div >
< div class = "line" > < a id = "l00122" name = "l00122" > < / a > < span class = "lineno" > 122< / span > < span class = "keywordflow" > return< / span > result;< / div >
< div class = "line" > < a id = "l00123" name = "l00123" > < / a > < span class = "lineno" > 123< / span > }< / div >
< div class = "line" > < a id = "l00124" name = "l00124" > < / a > < span class = "lineno" > 124< / span > < span class = "preprocessor" > #endif< / span > < / div >
< div class = "line" > < a id = "l00125" name = "l00125" > < / a > < span class = "lineno" > 125< / span > < / div >
< div class = "line" > < a id = "l00126" name = "l00126" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a111f44b9b9cf67a8e8d83794ac9f5291" > 126< / a > < / span > < span class = "keyword" > inline< / span > int64_t < a class = "code hl_function" href = "namespaceoperations__research.html#a111f44b9b9cf67a8e8d83794ac9f5291" > CapAdd< / a > (int64_t x, int64_t y) {< / div >
< div class = "line" > < a id = "l00127" name = "l00127" > < / a > < span class = "lineno" > 127< / span > < span class = "preprocessor" > #if defined(__GNUC__) & & defined(__x86_64__)< / span > < / div >
< div class = "line" > < a id = "l00128" name = "l00128" > < / a > < span class = "lineno" > 128< / span > < span class = "keywordflow" > return< / span > CapAddFast(x, y);< / div >
< div class = "line" > < a id = "l00129" name = "l00129" > < / a > < span class = "lineno" > 129< / span > < span class = "preprocessor" > #else< / span > < / div >
< div class = "line" > < a id = "l00130" name = "l00130" > < / a > < span class = "lineno" > 130< / span > < span class = "keywordflow" > return< / span > < a class = "code hl_function" href = "namespaceoperations__research.html#a92790ebe58f31601890072ac2d4911c5" > CapAddGeneric< / a > (x, y);< / div >
< div class = "line" > < a id = "l00131" name = "l00131" > < / a > < span class = "lineno" > 131< / span > < span class = "preprocessor" > #endif< / span > < / div >
< div class = "line" > < a id = "l00132" name = "l00132" > < / a > < span class = "lineno" > 132< / span > }< / div >
< div class = "line" > < a id = "l00133" name = "l00133" > < / a > < span class = "lineno" > 133< / span > < / div >
< div class = "line" > < a id = "l00134" name = "l00134" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a1e489359fd31c3ef24a113fce05c08ee" > 134< / a > < / span > < span class = "keyword" > inline< / span > < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "namespaceoperations__research.html#a1e489359fd31c3ef24a113fce05c08ee" > CapAddTo< / a > (int64_t x, int64_t* y) { *y = < a class = "code hl_function" href = "namespaceoperations__research.html#a111f44b9b9cf67a8e8d83794ac9f5291" > CapAdd< / a > (*y, x); }< / div >
< div class = "line" > < a id = "l00135" name = "l00135" > < / a > < span class = "lineno" > 135< / span > < / div >
< div class = "line" > < a id = "l00136" name = "l00136" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#af226a644c66eca0d1ce8885529f9f5a1" > 136< / a > < / span > < span class = "keyword" > inline< / span > int64_t < a class = "code hl_function" href = "namespaceoperations__research.html#af226a644c66eca0d1ce8885529f9f5a1" > CapSubGeneric< / a > (int64_t x, int64_t y) {< / div >
< div class = "line" > < a id = "l00137" name = "l00137" > < / a > < span class = "lineno" > 137< / span > < span class = "keyword" > const< / span > int64_t result = < a class = "code hl_function" href = "namespaceoperations__research.html#ab7f89c34e63aca5f186808225f45865b" > TwosComplementSubtraction< / a > (x, y);< / div >
< div class = "line" > < a id = "l00138" name = "l00138" > < / a > < span class = "lineno" > 138< / span > < span class = "keywordflow" > return< / span > < a class = "code hl_function" href = "namespaceoperations__research.html#ab5b3d385e40264b5c3094b64d10a2299" > SubHadOverflow< / a > (x, y, result) ? < a class = "code hl_function" href = "namespaceoperations__research.html#a28f4f86e4cc6cfc5e075577baabd00f2" > CapWithSignOf< / a > (x) : result;< / div >
< div class = "line" > < a id = "l00139" name = "l00139" > < / a > < span class = "lineno" > 139< / span > }< / div >
< div class = "line" > < a id = "l00140" name = "l00140" > < / a > < span class = "lineno" > 140< / span > < / div >
< div class = "line" > < a id = "l00141" name = "l00141" > < / a > < span class = "lineno" > 141< / span > < span class = "preprocessor" > #if defined(__GNUC__) & & defined(__x86_64__)< / span > < / div >
< div class = "line" > < a id = "l00142" name = "l00142" > < / a > < span class = "lineno" > 142< / span > < span class = "comment" > // TODO(user): port this to other architectures.< / span > < / div >
< div class = "line" > < a id = "l00143" name = "l00143" > < / a > < span class = "lineno" > 143< / span > < span class = "keyword" > inline< / span > int64_t CapSubFast(int64_t x, int64_t y) {< / div >
< div class = "line" > < a id = "l00144" name = "l00144" > < / a > < span class = "lineno" > 144< / span > < span class = "keyword" > const< / span > int64_t cap = < a class = "code hl_function" href = "namespaceoperations__research.html#a28f4f86e4cc6cfc5e075577baabd00f2" > CapWithSignOf< / a > (x);< / div >
< div class = "line" > < a id = "l00145" name = "l00145" > < / a > < span class = "lineno" > 145< / span > int64_t result = x;< / div >
< div class = "line" > < a id = "l00146" name = "l00146" > < / a > < span class = "lineno" > 146< / span > < span class = "comment" > // clang-format off< / span > < / div >
< div class = "line" > < a id = "l00147" name = "l00147" > < / a > < span class = "lineno" > 147< / span > < span class = "keyword" > asm< / span > < span class = "keyword" > volatile< / span > ( < span class = "comment" > // ' volatile' : ask compiler optimizer " keep as is" .< / span > < / div >
< div class = "line" > < a id = "l00148" name = "l00148" > < / a > < span class = "lineno" > 148< / span > < span class = "stringliteral" > " \t" < / span > < span class = "stringliteral" > " subq %[y],%[result]" < / span > < / div >
< div class = "line" > < a id = "l00149" name = "l00149" > < / a > < span class = "lineno" > 149< / span > < span class = "stringliteral" > " \n\t" < / span > < span class = "stringliteral" > " cmovoq %[cap],%[result]" < / span > < span class = "comment" > // Conditional move if overflow.< / span > < / div >
< div class = "line" > < a id = "l00150" name = "l00150" > < / a > < span class = "lineno" > 150< / span > : [result] < span class = "stringliteral" > " =r" < / span > (result) < span class = "comment" > // Output< / span > < / div >
< div class = "line" > < a id = "l00151" name = "l00151" > < / a > < span class = "lineno" > 151< / 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 >
< div class = "line" > < a id = "l00152" name = "l00152" > < / a > < span class = "lineno" > 152< / span > : < span class = "stringliteral" > " cc" < / span > < span class = "comment" > /* Clobbered registers */< / span > );< / div >
< div class = "line" > < a id = "l00153" name = "l00153" > < / a > < span class = "lineno" > 153< / span > < span class = "comment" > // clang-format on< / span > < / div >
< div class = "line" > < a id = "l00154" name = "l00154" > < / a > < span class = "lineno" > 154< / span > < span class = "keywordflow" > return< / span > result;< / div >
< div class = "line" > < a id = "l00155" name = "l00155" > < / a > < span class = "lineno" > 155< / span > }< / div >
< div class = "line" > < a id = "l00156" name = "l00156" > < / a > < span class = "lineno" > 156< / span > < span class = "preprocessor" > #endif< / span > < / div >
< div class = "line" > < a id = "l00157" name = "l00157" > < / a > < span class = "lineno" > 157< / span > < / div >
< div class = "line" > < a id = "l00158" name = "l00158" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a4a43d435871f16c321861fa5de32df82" > 158< / a > < / span > < span class = "keyword" > inline< / span > int64_t < a class = "code hl_function" href = "namespaceoperations__research.html#a4a43d435871f16c321861fa5de32df82" > CapSub< / a > (int64_t x, int64_t y) {< / div >
< div class = "line" > < a id = "l00159" name = "l00159" > < / a > < span class = "lineno" > 159< / span > < span class = "preprocessor" > #if defined(__GNUC__) & & defined(__x86_64__)< / span > < / div >
< div class = "line" > < a id = "l00160" name = "l00160" > < / a > < span class = "lineno" > 160< / span > < span class = "keywordflow" > return< / span > CapSubFast(x, y);< / div >
< div class = "line" > < a id = "l00161" name = "l00161" > < / a > < span class = "lineno" > 161< / span > < span class = "preprocessor" > #else< / span > < / div >
< div class = "line" > < a id = "l00162" name = "l00162" > < / a > < span class = "lineno" > 162< / span > < span class = "keywordflow" > return< / span > < a class = "code hl_function" href = "namespaceoperations__research.html#af226a644c66eca0d1ce8885529f9f5a1" > CapSubGeneric< / a > (x, y);< / div >
< div class = "line" > < a id = "l00163" name = "l00163" > < / a > < span class = "lineno" > 163< / span > < span class = "preprocessor" > #endif< / span > < / div >
< div class = "line" > < a id = "l00164" name = "l00164" > < / a > < span class = "lineno" > 164< / span > }< / div >
< div class = "line" > < a id = "l00165" name = "l00165" > < / a > < span class = "lineno" > 165< / span > < / div >
< div class = "line" > < a id = "l00166" name = "l00166" > < / a > < span class = "lineno" > 166< / span > < span class = "comment" > // Note(user): -kint64min != kint64max, but kint64max == ~kint64min.< / span > < / div >
< div class = "line" > < a id = "l00167" name = "l00167" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#af979bdbf1d7d690ae24e97ad456297d2" > 167< / a > < / span > < span class = "keyword" > inline< / span > int64_t < a class = "code hl_function" href = "namespaceoperations__research.html#af979bdbf1d7d690ae24e97ad456297d2" > CapOpp< / a > (int64_t v) { < span class = "keywordflow" > return< / span > v == < a class = "code hl_variable" href = "integral__types_8h.html#af8b05f1b3a4c4ef94dd184c6c31a56e6" > kint64min< / a > ? ~v : -v; }< / div >
< div class = "line" > < a id = "l00168" name = "l00168" > < / a > < span class = "lineno" > 168< / span > < / div >
< div class = "line" > < a id = "l00169" name = "l00169" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research_1_1cap__prod__util.html" > 169< / a > < / span > < span class = "keyword" > namespace < / span > cap_prod_util {< / div >
< div class = "line" > < a id = "l00170" name = "l00170" > < / a > < span class = "lineno" > 170< / span > < span class = "comment" > // Returns an unsigned int equal to the absolute value of n, in a way that< / span > < / div >
< div class = "line" > < a id = "l00171" name = "l00171" > < / a > < span class = "lineno" > 171< / span > < span class = "comment" > // will not produce overflows.< / span > < / div >
< div class = "line" > < a id = "l00172" name = "l00172" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research_1_1cap__prod__util.html#ad6bc7f73c7f1b8854f5a0c3f3bd02db5" > 172< / a > < / span > < span class = "keyword" > inline< / span > uint64_t < a class = "code hl_function" href = "namespaceoperations__research_1_1cap__prod__util.html#ad6bc7f73c7f1b8854f5a0c3f3bd02db5" > uint_abs< / a > (int64_t n) {< / div >
< div class = "line" > < a id = "l00173" name = "l00173" > < / a > < span class = "lineno" > 173< / span > < span class = "keywordflow" > return< / span > n < 0 ? ~static_cast< uint64_t> (n) + 1 : < span class = "keyword" > static_cast< < / span > uint64_t< span class = "keyword" > > < / span > (n);< / div >
< div class = "line" > < a id = "l00174" name = "l00174" > < / a > < span class = "lineno" > 174< / span > }< / div >
< div class = "line" > < a id = "l00175" name = "l00175" > < / a > < span class = "lineno" > 175< / span > } < span class = "comment" > // namespace cap_prod_util< / span > < / div >
< div class = "line" > < a id = "l00176" name = "l00176" > < / a > < span class = "lineno" > 176< / span > < / div >
< div class = "line" > < a id = "l00177" name = "l00177" > < / a > < span class = "lineno" > 177< / span > < span class = "comment" > // The generic algorithm computes a bound on the number of bits necessary to< / span > < / div >
< div class = "line" > < a id = "l00178" name = "l00178" > < / a > < span class = "lineno" > 178< / span > < span class = "comment" > // store the result. For this it uses the position of the most significant bits< / span > < / div >
< div class = "line" > < a id = "l00179" name = "l00179" > < / a > < span class = "lineno" > 179< / span > < span class = "comment" > // of each of the arguments.< / span > < / div >
< div class = "line" > < a id = "l00180" name = "l00180" > < / a > < span class = "lineno" > 180< / span > < span class = "comment" > // If the result needs at least 64 bits, then return a capped value.< / span > < / div >
< div class = "line" > < a id = "l00181" name = "l00181" > < / a > < span class = "lineno" > 181< / span > < span class = "comment" > // If the result needs at most 63 bits, then return the product.< / span > < / div >
< div class = "line" > < a id = "l00182" name = "l00182" > < / a > < span class = "lineno" > 182< / span > < span class = "comment" > // Otherwise, the result may use 63 or 64 bits: compute the product< / span > < / div >
< div class = "line" > < a id = "l00183" name = "l00183" > < / a > < span class = "lineno" > 183< / span > < span class = "comment" > // as a uint64_t, and cap it if necessary.< / span > < / div >
< div class = "line" > < a id = "l00184" name = "l00184" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#adfcad7c607afe2de123ac91fcd2b87c0" > 184< / a > < / span > < span class = "keyword" > inline< / span > int64_t < a class = "code hl_function" href = "namespaceoperations__research.html#adfcad7c607afe2de123ac91fcd2b87c0" > CapProdGeneric< / a > (int64_t x, int64_t y) {< / div >
< div class = "line" > < a id = "l00185" name = "l00185" > < / a > < span class = "lineno" > 185< / span > < span class = "keyword" > const< / span > uint64_t < a class = "code hl_variable" href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > = < a class = "code hl_function" href = "namespaceoperations__research_1_1cap__prod__util.html#ad6bc7f73c7f1b8854f5a0c3f3bd02db5" > cap_prod_util::uint_abs< / a > (x);< / div >
< div class = "line" > < a id = "l00186" name = "l00186" > < / a > < span class = "lineno" > 186< / span > < span class = "keyword" > const< / span > uint64_t < a class = "code hl_variable" href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > = < a class = "code hl_function" href = "namespaceoperations__research_1_1cap__prod__util.html#ad6bc7f73c7f1b8854f5a0c3f3bd02db5" > cap_prod_util::uint_abs< / a > (y);< / div >
< div class = "line" > < a id = "l00187" name = "l00187" > < / a > < span class = "lineno" > 187< / span > < span class = "comment" > // Let MSB(x) denote the most significant bit of x. We have:< / span > < / div >
< div class = "line" > < a id = "l00188" name = "l00188" > < / a > < span class = "lineno" > 188< / span > < span class = "comment" > // MSB(x) + MSB(y) < = MSB(x * y) < = MSB(x) + MSB(y) + 1< / span > < / div >
< div class = "line" > < a id = "l00189" name = "l00189" > < / a > < span class = "lineno" > 189< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > msb_sum =< / div >
< div class = "line" > < a id = "l00190" name = "l00190" > < / a > < span class = "lineno" > 190< / span > < a class = "code hl_function" href = "namespaceoperations__research.html#afa6ef9aef70f95b9d5bcee2c10937bc8" > MostSignificantBitPosition64< / a > (< a class = "code hl_variable" href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > ) + < a class = "code hl_function" href = "namespaceoperations__research.html#afa6ef9aef70f95b9d5bcee2c10937bc8" > MostSignificantBitPosition64< / a > (< a class = "code hl_variable" href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > );< / div >
< div class = "line" > < a id = "l00191" name = "l00191" > < / a > < span class = "lineno" > 191< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > kMaxBitIndexInInt64 = 63;< / div >
< div class = "line" > < a id = "l00192" name = "l00192" > < / a > < span class = "lineno" > 192< / span > < span class = "keywordflow" > if< / span > (msb_sum < = kMaxBitIndexInInt64 - 2) < span class = "keywordflow" > return< / span > x * y;< / div >
< div class = "line" > < a id = "l00193" name = "l00193" > < / a > < span class = "lineno" > 193< / span > < span class = "comment" > // Catch a == 0 or b == 0 now, as MostSignificantBitPosition64(0) == 0.< / span > < / div >
< div class = "line" > < a id = "l00194" name = "l00194" > < / a > < span class = "lineno" > 194< / span > < span class = "comment" > // TODO(user): avoid this by writing function Log2(a) with Log2(0) == -1.< / span > < / div >
< div class = "line" > < a id = "l00195" name = "l00195" > < / a > < span class = "lineno" > 195< / span > < span class = "keywordflow" > if< / span > (< a class = "code hl_variable" href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > == 0 || < a class = "code hl_variable" href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > == 0) < span class = "keywordflow" > return< / span > 0;< / div >
< div class = "line" > < a id = "l00196" name = "l00196" > < / a > < span class = "lineno" > 196< / span > < span class = "keyword" > const< / span > int64_t cap = < a class = "code hl_function" href = "namespaceoperations__research.html#a28f4f86e4cc6cfc5e075577baabd00f2" > CapWithSignOf< / a > (x ^ y);< / div >
< div class = "line" > < a id = "l00197" name = "l00197" > < / a > < span class = "lineno" > 197< / span > < span class = "keywordflow" > if< / span > (msb_sum > = kMaxBitIndexInInt64) < span class = "keywordflow" > return< / span > cap;< / div >
< div class = "line" > < a id = "l00198" name = "l00198" > < / a > < span class = "lineno" > 198< / span > < span class = "comment" > // The corner case is when msb_sum == 62, i.e. at least 63 bits will be< / span > < / div >
< div class = "line" > < a id = "l00199" name = "l00199" > < / a > < span class = "lineno" > 199< / span > < span class = "comment" > // needed to store the product. The following product will never overflow< / span > < / div >
< div class = "line" > < a id = "l00200" name = "l00200" > < / a > < span class = "lineno" > 200< / span > < span class = "comment" > // on uint64_t, since msb_sum == 62.< / span > < / div >
< div class = "line" > < a id = "l00201" name = "l00201" > < / a > < span class = "lineno" > 201< / span > < span class = "keyword" > const< / span > uint64_t u_prod = < a class = "code hl_variable" href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > * < a class = "code hl_variable" href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > ;< / div >
< div class = "line" > < a id = "l00202" name = "l00202" > < / a > < span class = "lineno" > 202< / span > < span class = "comment" > // The overflow cases are captured by one of the following conditions:< / span > < / div >
< div class = "line" > < a id = "l00203" name = "l00203" > < / a > < span class = "lineno" > 203< / span > < span class = "comment" > // (cap > = 0 & & u_prod > = static_cast< uint64_t> (kint64max) or< / span > < / div >
< div class = "line" > < a id = "l00204" name = "l00204" > < / a > < span class = "lineno" > 204< / span > < span class = "comment" > // (cap < 0 & & u_prod > = static_cast< uint64_t> (kint64min)).< / span > < / div >
< div class = "line" > < a id = "l00205" name = "l00205" > < / a > < span class = "lineno" > 205< / span > < span class = "comment" > // These can be optimized as follows (and if the condition is false, it is< / span > < / div >
< div class = "line" > < a id = "l00206" name = "l00206" > < / a > < span class = "lineno" > 206< / span > < span class = "comment" > // safe to compute x * y.< / span > < / div >
< div class = "line" > < a id = "l00207" name = "l00207" > < / a > < span class = "lineno" > 207< / span > < span class = "keywordflow" > if< / span > (u_prod > = < span class = "keyword" > static_cast< < / span > uint64_t< span class = "keyword" > > < / span > (cap)) < span class = "keywordflow" > return< / span > cap;< / div >
< div class = "line" > < a id = "l00208" name = "l00208" > < / a > < span class = "lineno" > 208< / span > < span class = "keyword" > const< / span > int64_t abs_result = absl::bit_cast< int64_t> (u_prod);< / div >
< div class = "line" > < a id = "l00209" name = "l00209" > < / a > < span class = "lineno" > 209< / span > < span class = "keywordflow" > return< / span > cap < 0 ? -abs_result : abs_result;< / div >
< div class = "line" > < a id = "l00210" name = "l00210" > < / a > < span class = "lineno" > 210< / span > }< / div >
< div class = "line" > < a id = "l00211" name = "l00211" > < / a > < span class = "lineno" > 211< / span > < / div >
< div class = "line" > < a id = "l00212" name = "l00212" > < / a > < span class = "lineno" > 212< / span > < span class = "preprocessor" > #if defined(__GNUC__) & & defined(__x86_64__)< / span > < / div >
< div class = "line" > < a id = "l00213" name = "l00213" > < / a > < span class = "lineno" > 213< / span > < span class = "comment" > // TODO(user): port this to other architectures.< / span > < / div >
< div class = "line" > < a id = "l00214" name = "l00214" > < / a > < span class = "lineno" > 214< / span > < span class = "keyword" > inline< / span > int64_t CapProdFast(int64_t x, int64_t y) {< / div >
< div class = "line" > < a id = "l00215" name = "l00215" > < / a > < span class = "lineno" > 215< / span > < span class = "comment" > // cap = kint64max if x and y have the same sign, cap = kint64min< / span > < / div >
< div class = "line" > < a id = "l00216" name = "l00216" > < / a > < span class = "lineno" > 216< / span > < span class = "comment" > // otherwise.< / span > < / div >
< div class = "line" > < a id = "l00217" name = "l00217" > < / a > < span class = "lineno" > 217< / span > < span class = "keyword" > const< / span > int64_t cap = < a class = "code hl_function" href = "namespaceoperations__research.html#a28f4f86e4cc6cfc5e075577baabd00f2" > CapWithSignOf< / a > (x ^ y);< / div >
< div class = "line" > < a id = "l00218" name = "l00218" > < / a > < span class = "lineno" > 218< / span > int64_t result = x;< / div >
< div class = "line" > < a id = "l00219" name = "l00219" > < / a > < span class = "lineno" > 219< / span > < span class = "comment" > // Here, we use the fact that imul of two signed 64-integers returns a 128-bit< / span > < / div >
< div class = "line" > < a id = "l00220" name = "l00220" > < / a > < span class = "lineno" > 220< / span > < span class = "comment" > // result -- we care about the lower 64 bits. More importantly, imul also sets< / span > < / div >
< div class = "line" > < a id = "l00221" name = "l00221" > < / a > < span class = "lineno" > 221< / span > < span class = "comment" > // the carry flag if 64 bits were not enough.< / span > < / div >
< div class = "line" > < a id = "l00222" name = "l00222" > < / a > < span class = "lineno" > 222< / span > < span class = "comment" > // We therefore use cmovc to return cap if the carry was set.< / span > < / div >
< div class = "line" > < a id = "l00223" name = "l00223" > < / a > < span class = "lineno" > 223< / span > < span class = "comment" > // clang-format off< / span > < / div >
< div class = "line" > < a id = "l00224" name = "l00224" > < / a > < span class = "lineno" > 224< / span > < span class = "keyword" > asm< / span > < span class = "keyword" > volatile< / span > ( < span class = "comment" > // ' volatile' : ask compiler optimizer " keep as is" .< / span > < / div >
< div class = "line" > < a id = "l00225" name = "l00225" > < / a > < span class = "lineno" > 225< / span > < span class = "stringliteral" > " \n\t" < / span > < span class = "stringliteral" > " imulq %[y],%[result]" < / span > < / div >
< div class = "line" > < a id = "l00226" name = "l00226" > < / a > < span class = "lineno" > 226< / span > < span class = "stringliteral" > " \n\t" < / span > < span class = "stringliteral" > " cmovcq %[cap],%[result]" < / span > < span class = "comment" > // Conditional move if carry.< / span > < / div >
< div class = "line" > < a id = "l00227" name = "l00227" > < / a > < span class = "lineno" > 227< / span > : [result] < span class = "stringliteral" > " =r" < / span > (result) < span class = "comment" > // Output< / span > < / div >
< div class = "line" > < a id = "l00228" name = "l00228" > < / a > < span class = "lineno" > 228< / 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 >
< div class = "line" > < a id = "l00229" name = "l00229" > < / a > < span class = "lineno" > 229< / span > : < span class = "stringliteral" > " cc" < / span > < span class = "comment" > /* Clobbered registers */< / span > );< / div >
< div class = "line" > < a id = "l00230" name = "l00230" > < / a > < span class = "lineno" > 230< / span > < span class = "comment" > // clang-format on< / span > < / div >
< div class = "line" > < a id = "l00231" name = "l00231" > < / a > < span class = "lineno" > 231< / span > < span class = "keywordflow" > return< / span > result;< / div >
< div class = "line" > < a id = "l00232" name = "l00232" > < / a > < span class = "lineno" > 232< / span > }< / div >
< div class = "line" > < a id = "l00233" name = "l00233" > < / a > < span class = "lineno" > 233< / span > < span class = "preprocessor" > #endif< / span > < / div >
< div class = "line" > < a id = "l00234" name = "l00234" > < / a > < span class = "lineno" > 234< / span > < / div >
< div class = "line" > < a id = "l00235" name = "l00235" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#aa64bf49d041052c7cb3f40f7496d7534" > 235< / a > < / span > < span class = "keyword" > inline< / span > int64_t < a class = "code hl_function" href = "namespaceoperations__research.html#aa64bf49d041052c7cb3f40f7496d7534" > CapProd< / a > (int64_t x, int64_t y) {< / div >
< div class = "line" > < a id = "l00236" name = "l00236" > < / a > < span class = "lineno" > 236< / span > < span class = "preprocessor" > #if defined(__GNUC__) & & defined(__x86_64__)< / span > < / div >
< div class = "line" > < a id = "l00237" name = "l00237" > < / a > < span class = "lineno" > 237< / span > < span class = "keywordflow" > return< / span > CapProdFast(x, y);< / div >
< div class = "line" > < a id = "l00238" name = "l00238" > < / a > < span class = "lineno" > 238< / span > < span class = "preprocessor" > #else< / span > < / div >
< div class = "line" > < a id = "l00239" name = "l00239" > < / a > < span class = "lineno" > 239< / span > < span class = "keywordflow" > return< / span > < a class = "code hl_function" href = "namespaceoperations__research.html#adfcad7c607afe2de123ac91fcd2b87c0" > CapProdGeneric< / a > (x, y);< / div >
< div class = "line" > < a id = "l00240" name = "l00240" > < / a > < span class = "lineno" > 240< / span > < span class = "preprocessor" > #endif< / span > < / div >
< div class = "line" > < a id = "l00241" name = "l00241" > < / a > < span class = "lineno" > 241< / span > }< / div >
< div class = "line" > < a id = "l00242" name = "l00242" > < / a > < span class = "lineno" > 242< / span > } < span class = "comment" > // namespace operations_research< / span > < / div >
< div class = "line" > < a id = "l00243" name = "l00243" > < / a > < span class = "lineno" > 243< / span > < / div >
< div class = "line" > < a id = "l00244" name = "l00244" > < / a > < span class = "lineno" > 244< / span > < span class = "preprocessor" > #endif < / span > < span class = "comment" > // OR_TOOLS_UTIL_SATURATED_ARITHMETIC_H_< / span > < / div >
2022-03-04 00:11:33 +01:00
< div class = "ttc" id = "abase_2logging_8h_html_ae89df3243bbb8341130c7b3f44145ea0" > < div class = "ttname" > < a href = "base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0" > DCHECK_EQ< / a > < / div > < div class = "ttdeci" > #define DCHECK_EQ(val1, val2)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "base_2logging_8h_source.html#l00891" > base/logging.h:891< / a > < / div > < / div >
2022-01-17 21:42:14 +01:00
< div class = "ttc" id = "abitset_8h_html" > < div class = "ttname" > < a href = "bitset_8h.html" > bitset.h< / a > < / div > < / div >
< div class = "ttc" id = "aconstraint__solver_2table_8cc_html_a9293e4d29cac928301645070dd307683" > < div class = "ttname" > < a href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > < / div > < div class = "ttdeci" > int64_t b< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "constraint__solver_2table_8cc_source.html#l00047" > constraint_solver/table.cc:47< / a > < / div > < / div >
< div class = "ttc" id = "aconstraint__solver_2table_8cc_html_acb18315d548212835cd8ed4287e6c0b6" > < div class = "ttname" > < a href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > < / div > < div class = "ttdeci" > int64_t a< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "constraint__solver_2table_8cc_source.html#l00046" > constraint_solver/table.cc:46< / a > < / div > < / div >
< div class = "ttc" id = "aintegral__types_8h_html" > < div class = "ttname" > < a href = "integral__types_8h.html" > integral_types.h< / a > < / div > < / div >
< div class = "ttc" id = "aintegral__types_8h_html_a808bd435380aa1e2bbd6f13ac7759897" > < div class = "ttname" > < a href = "integral__types_8h.html#a808bd435380aa1e2bbd6f13ac7759897" > kint64max< / a > < / div > < div class = "ttdeci" > static const int64_t kint64max< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "integral__types_8h_source.html#l00032" > integral_types.h:32< / a > < / div > < / div >
< div class = "ttc" id = "aintegral__types_8h_html_af8b05f1b3a4c4ef94dd184c6c31a56e6" > < div class = "ttname" > < a href = "integral__types_8h.html#af8b05f1b3a4c4ef94dd184c6c31a56e6" > kint64min< / a > < / div > < div class = "ttdeci" > static const int64_t kint64min< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "integral__types_8h_source.html#l00031" > integral_types.h:31< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_1_1cap__prod__util_html_ad6bc7f73c7f1b8854f5a0c3f3bd02db5" > < div class = "ttname" > < a href = "namespaceoperations__research_1_1cap__prod__util.html#ad6bc7f73c7f1b8854f5a0c3f3bd02db5" > operations_research::cap_prod_util::uint_abs< / a > < / div > < div class = "ttdeci" > uint64_t uint_abs(int64_t n)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "saturated__arithmetic_8h_source.html#l00172" > saturated_arithmetic.h:172< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html" > < div class = "ttname" > < a href = "namespaceoperations__research.html" > operations_research< / a > < / div > < div class = "ttdoc" > Collection of objects used to extend the Constraint Solver library.< / 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 >
< div class = "ttc" id = "anamespaceoperations__research_html_a0004fd13375ee41f234051cb5cc74869" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a0004fd13375ee41f234051cb5cc74869" > operations_research::SubOverflows< / a > < / div > < div class = "ttdeci" > int64_t SubOverflows(int64_t x, int64_t y)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "saturated__arithmetic_8h_source.html#l00082" > saturated_arithmetic.h:82< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_a0d130d7d0baf49b66a6938714828d0aa" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a0d130d7d0baf49b66a6938714828d0aa" > operations_research::AddHadOverflow< / a > < / div > < div class = "ttdeci" > bool AddHadOverflow(int64_t x, int64_t y, int64_t sum)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "saturated__arithmetic_8h_source.html#l00054" > saturated_arithmetic.h:54< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_a111f44b9b9cf67a8e8d83794ac9f5291" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a111f44b9b9cf67a8e8d83794ac9f5291" > operations_research::CapAdd< / a > < / div > < div class = "ttdeci" > int64_t CapAdd(int64_t x, int64_t y)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "saturated__arithmetic_8h_source.html#l00126" > saturated_arithmetic.h:126< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_a1e489359fd31c3ef24a113fce05c08ee" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a1e489359fd31c3ef24a113fce05c08ee" > operations_research::CapAddTo< / a > < / div > < div class = "ttdeci" > void CapAddTo(int64_t x, int64_t *y)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "saturated__arithmetic_8h_source.html#l00134" > saturated_arithmetic.h:134< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_a28f4f86e4cc6cfc5e075577baabd00f2" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a28f4f86e4cc6cfc5e075577baabd00f2" > operations_research::CapWithSignOf< / a > < / div > < div class = "ttdeci" > int64_t CapWithSignOf(int64_t x)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "saturated__arithmetic_8h_source.html#l00099" > saturated_arithmetic.h:99< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_a2e03c61d96b37a3533c3ffcec93fc18d" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a2e03c61d96b37a3533c3ffcec93fc18d" > operations_research::TwosComplementAddition< / a > < / div > < div class = "ttdeci" > int64_t TwosComplementAddition(int64_t x, int64_t y)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "saturated__arithmetic_8h_source.html#l00038" > saturated_arithmetic.h:38< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_a4a43d435871f16c321861fa5de32df82" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a4a43d435871f16c321861fa5de32df82" > operations_research::CapSub< / a > < / div > < div class = "ttdeci" > int64_t CapSub(int64_t x, int64_t y)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "saturated__arithmetic_8h_source.html#l00158" > saturated_arithmetic.h:158< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_a92790ebe58f31601890072ac2d4911c5" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a92790ebe58f31601890072ac2d4911c5" > operations_research::CapAddGeneric< / a > < / div > < div class = "ttdeci" > int64_t CapAddGeneric(int64_t x, int64_t y)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "saturated__arithmetic_8h_source.html#l00104" > saturated_arithmetic.h:104< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_a93bd93f028c18a4b55b30056ef60df44" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a93bd93f028c18a4b55b30056ef60df44" > operations_research::AddOverflows< / a > < / div > < div class = "ttdeci" > bool AddOverflows(int64_t x, int64_t y)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "saturated__arithmetic_8h_source.html#l00078" > saturated_arithmetic.h:78< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_aa64bf49d041052c7cb3f40f7496d7534" > < div class = "ttname" > < a href = "namespaceoperations__research.html#aa64bf49d041052c7cb3f40f7496d7534" > operations_research::CapProd< / a > < / div > < div class = "ttdeci" > int64_t CapProd(int64_t x, int64_t y)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "saturated__arithmetic_8h_source.html#l00235" > saturated_arithmetic.h:235< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_ab5b3d385e40264b5c3094b64d10a2299" > < div class = "ttname" > < a href = "namespaceoperations__research.html#ab5b3d385e40264b5c3094b64d10a2299" > operations_research::SubHadOverflow< / a > < / div > < div class = "ttdeci" > bool SubHadOverflow(int64_t x, int64_t y, int64_t diff)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "saturated__arithmetic_8h_source.html#l00063" > saturated_arithmetic.h:63< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_ab7f89c34e63aca5f186808225f45865b" > < div class = "ttname" > < a href = "namespaceoperations__research.html#ab7f89c34e63aca5f186808225f45865b" > operations_research::TwosComplementSubtraction< / a > < / div > < div class = "ttdeci" > int64_t TwosComplementSubtraction(int64_t x, int64_t y)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "saturated__arithmetic_8h_source.html#l00045" > saturated_arithmetic.h:45< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_adfcad7c607afe2de123ac91fcd2b87c0" > < div class = "ttname" > < a href = "namespaceoperations__research.html#adfcad7c607afe2de123ac91fcd2b87c0" > operations_research::CapProdGeneric< / a > < / div > < div class = "ttdeci" > int64_t CapProdGeneric(int64_t x, int64_t y)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "saturated__arithmetic_8h_source.html#l00184" > saturated_arithmetic.h:184< / a > < / div > < / div >
< 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#l00089" > saturated_arithmetic.h:89< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_af226a644c66eca0d1ce8885529f9f5a1" > < div class = "ttname" > < a href = "namespaceoperations__research.html#af226a644c66eca0d1ce8885529f9f5a1" > operations_research::CapSubGeneric< / a > < / div > < div class = "ttdeci" > int64_t CapSubGeneric(int64_t x, int64_t y)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "saturated__arithmetic_8h_source.html#l00136" > saturated_arithmetic.h:136< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_af979bdbf1d7d690ae24e97ad456297d2" > < div class = "ttname" > < a href = "namespaceoperations__research.html#af979bdbf1d7d690ae24e97ad456297d2" > operations_research::CapOpp< / a > < / div > < div class = "ttdeci" > int64_t CapOpp(int64_t v)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "saturated__arithmetic_8h_source.html#l00167" > saturated_arithmetic.h:167< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_afa6ef9aef70f95b9d5bcee2c10937bc8" > < div class = "ttname" > < a href = "namespaceoperations__research.html#afa6ef9aef70f95b9d5bcee2c10937bc8" > operations_research::MostSignificantBitPosition64< / a > < / div > < div class = "ttdeci" > int MostSignificantBitPosition64(uint64_t n)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "bitset_8h_source.html#l00231" > bitset.h:231< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
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2020-09-02 09:42:51 +02:00
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