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< a href = "mathutil_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 2010-2021 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 >
< 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 >
< 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 >
< div class = "line" > < a name = "l00005" > < / a > < span class = "lineno" > 5< / span >   < span class = "comment" > //< / span > < / div >
< 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 >
< div class = "line" > < a name = "l00007" > < / a > < span class = "lineno" > 7< / span >   < span class = "comment" > //< / span > < / div >
< 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 >
< 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 >
< 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 >
< 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 >
< 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 = "l00014" > < / a > < span class = "lineno" > 14< / span >   < span class = "preprocessor" > #ifndef OR_TOOLS_BASE_MATHUTIL_H_< / span > < / div >
< div class = "line" > < a name = "l00015" > < / a > < span class = "lineno" > 15< / span >   < span class = "preprocessor" > #define OR_TOOLS_BASE_MATHUTIL_H_< / span > < / div >
< div class = "line" > < a name = "l00016" > < / a > < span class = "lineno" > 16< / span >   < / div >
< div class = "line" > < a name = "l00017" > < / a > < span class = "lineno" > 17< / span >   < span class = "preprocessor" > #include < math.h> < / span > < / div >
< div class = "line" > < a name = "l00018" > < / a > < span class = "lineno" > 18< / span >   < / div >
< div class = "line" > < a name = "l00019" > < / a > < span class = "lineno" > 19< / span >   < span class = "preprocessor" > #include < algorithm> < / span > < / div >
< div class = "line" > < a name = "l00020" > < / a > < span class = "lineno" > 20< / span >   < span class = "preprocessor" > #include < vector> < / span > < / div >
< div class = "line" > < a name = "l00021" > < / a > < span class = "lineno" > 21< / span >   < / div >
< div class = "line" > < a name = "l00022" > < / a > < span class = "lineno" > 22< / span >   < span class = "preprocessor" > #include " absl/base/casts.h" < / span > < / div >
< div class = "line" > < a name = "l00023" > < / a > < span class = "lineno" > 23< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "basictypes_8h.html" > ortools/base/basictypes.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00024" > < / a > < span class = "lineno" > 24< / 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 name = "l00025" > < / a > < span class = "lineno" > 25< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "base_2logging_8h.html" > ortools/base/logging.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00026" > < / a > < span class = "lineno" > 26< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "macros_8h.html" > ortools/base/macros.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00027" > < / a > < span class = "lineno" > 27< / span >   < / div >
< div class = "line" > < a name = "l00028" > < / a > < span class = "lineno" > 28< / 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 = "l00029" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_math_util.html" > 29< / a > < / span >   < span class = "keyword" > class < / span > < a class = "code" href = "classoperations__research_1_1_math_util.html" > MathUtil< / a > {< / div >
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< div class = "line" > < a name = "l00030" > < / a > < span class = "lineno" > 30< / span >   < span class = "keyword" > public< / span > :< / div >
< div class = "line" > < a name = "l00031" > < / a > < span class = "lineno" > 31< / span >   < span class = "comment" > // CeilOfRatio< IntegralType> < / span > < / div >
< div class = "line" > < a name = "l00032" > < / a > < span class = "lineno" > 32< / span >   < span class = "comment" > // FloorOfRatio< IntegralType> < / span > < / div >
< div class = "line" > < a name = "l00033" > < / a > < span class = "lineno" > 33< / span >   < span class = "comment" > // Returns the ceil (resp. floor) of the ratio of two integers.< / span > < / div >
< div class = "line" > < a name = "l00034" > < / a > < span class = "lineno" > 34< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00035" > < / a > < span class = "lineno" > 35< / span >   < span class = "comment" > // IntegralType: any integral type, whether signed or not.< / span > < / div >
< div class = "line" > < a name = "l00036" > < / a > < span class = "lineno" > 36< / span >   < span class = "comment" > // numerator: any integer: positive, negative, or zero.< / span > < / div >
< div class = "line" > < a name = "l00037" > < / a > < span class = "lineno" > 37< / span >   < span class = "comment" > // denominator: a non-zero integer, positive or negative.< / span > < / div >
< div class = "line" > < a name = "l00038" > < / a > < span class = "lineno" > 38< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > IntegralType> < / div >
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< div class = "line" > < a name = "l00039" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_math_util.html#a0cfaf8b139304c54e3403d4ffbd60157" > 39< / a > < / span >   < span class = "keyword" > static< / span > IntegralType < a class = "code" href = "classoperations__research_1_1_math_util.html#a0cfaf8b139304c54e3403d4ffbd60157" > CeilOfRatio< / a > (IntegralType numerator,< / div >
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< div class = "line" > < a name = "l00040" > < / a > < span class = "lineno" > 40< / span >   IntegralType denominator) {< / div >
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< div class = "line" > < a name = "l00041" > < / a > < span class = "lineno" > 41< / span >   < a class = "code" href = "base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0" > DCHECK_NE< / a > (0, denominator);< / div >
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< div class = "line" > < a name = "l00042" > < / a > < span class = "lineno" > 42< / span >   < span class = "keyword" > const< / span > IntegralType rounded_toward_zero = numerator / denominator;< / div >
< div class = "line" > < a name = "l00043" > < / a > < span class = "lineno" > 43< / span >   < span class = "keyword" > const< / span > IntegralType intermediate_product = rounded_toward_zero * denominator;< / div >
< div class = "line" > < a name = "l00044" > < / a > < span class = "lineno" > 44< / span >   < span class = "keyword" > const< / span > < span class = "keywordtype" > bool< / span > needs_adjustment =< / div >
< div class = "line" > < a name = "l00045" > < / a > < span class = "lineno" > 45< / span >   (rounded_toward_zero > = 0) & & < / div >
< div class = "line" > < a name = "l00046" > < / a > < span class = "lineno" > 46< / span >   ((denominator > 0 & & numerator > intermediate_product) ||< / div >
< div class = "line" > < a name = "l00047" > < / a > < span class = "lineno" > 47< / span >   (denominator < 0 & & numerator < intermediate_product));< / div >
< div class = "line" > < a name = "l00048" > < / a > < span class = "lineno" > 48< / span >   < span class = "keyword" > const< / span > IntegralType adjustment = < span class = "keyword" > static_cast< < / span > IntegralType< span class = "keyword" > > < / span > (needs_adjustment);< / div >
< div class = "line" > < a name = "l00049" > < / a > < span class = "lineno" > 49< / span >   < span class = "keyword" > const< / span > IntegralType ceil_of_ratio = rounded_toward_zero + adjustment;< / div >
< div class = "line" > < a name = "l00050" > < / a > < span class = "lineno" > 50< / span >   < span class = "keywordflow" > return< / span > ceil_of_ratio;< / div >
< div class = "line" > < a name = "l00051" > < / a > < span class = "lineno" > 51< / span >   }< / div >
< div class = "line" > < a name = "l00052" > < / a > < span class = "lineno" > 52< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > IntegralType> < / div >
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< div class = "line" > < a name = "l00053" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_math_util.html#a9e5c13b72c36481ed098c05031d1f850" > 53< / a > < / span >   < span class = "keyword" > static< / span > IntegralType < a class = "code" href = "classoperations__research_1_1_math_util.html#a9e5c13b72c36481ed098c05031d1f850" > FloorOfRatio< / a > (IntegralType numerator,< / div >
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< div class = "line" > < a name = "l00054" > < / a > < span class = "lineno" > 54< / span >   IntegralType denominator) {< / div >
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< div class = "line" > < a name = "l00055" > < / a > < span class = "lineno" > 55< / span >   < a class = "code" href = "base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0" > DCHECK_NE< / a > (0, denominator);< / div >
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< div class = "line" > < a name = "l00056" > < / a > < span class = "lineno" > 56< / span >   < span class = "keyword" > const< / span > IntegralType rounded_toward_zero = numerator / denominator;< / div >
< div class = "line" > < a name = "l00057" > < / a > < span class = "lineno" > 57< / span >   < span class = "keyword" > const< / span > IntegralType intermediate_product = rounded_toward_zero * denominator;< / div >
< div class = "line" > < a name = "l00058" > < / a > < span class = "lineno" > 58< / span >   < span class = "keyword" > const< / span > < span class = "keywordtype" > bool< / span > needs_adjustment =< / div >
< div class = "line" > < a name = "l00059" > < / a > < span class = "lineno" > 59< / span >   (rounded_toward_zero < = 0) & & < / div >
< div class = "line" > < a name = "l00060" > < / a > < span class = "lineno" > 60< / span >   ((denominator > 0 & & numerator < intermediate_product) ||< / div >
< div class = "line" > < a name = "l00061" > < / a > < span class = "lineno" > 61< / span >   (denominator < 0 & & numerator > intermediate_product));< / div >
< div class = "line" > < a name = "l00062" > < / a > < span class = "lineno" > 62< / span >   < span class = "keyword" > const< / span > IntegralType adjustment = < span class = "keyword" > static_cast< < / span > IntegralType< span class = "keyword" > > < / span > (needs_adjustment);< / div >
< div class = "line" > < a name = "l00063" > < / a > < span class = "lineno" > 63< / span >   < span class = "keyword" > const< / span > IntegralType floor_of_ratio = rounded_toward_zero - adjustment;< / div >
< div class = "line" > < a name = "l00064" > < / a > < span class = "lineno" > 64< / span >   < span class = "keywordflow" > return< / span > floor_of_ratio;< / div >
< div class = "line" > < a name = "l00065" > < / a > < span class = "lineno" > 65< / span >   }< / div >
< div class = "line" > < a name = "l00066" > < / a > < span class = "lineno" > 66< / span >   < / div >
< div class = "line" > < a name = "l00067" > < / a > < span class = "lineno" > 67< / span >   < span class = "comment" > // Returns the greatest common divisor of two unsigned integers x and y.< / span > < / div >
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< div class = "line" > < a name = "l00068" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_math_util.html#a5677e679e0d095f4cfb0a61d213ccdd7" > 68< / a > < / span >   < span class = "keyword" > static< / span > < span class = "keywordtype" > unsigned< / span > < span class = "keywordtype" > int< / span > < a class = "code" href = "classoperations__research_1_1_math_util.html#a5677e679e0d095f4cfb0a61d213ccdd7" > GCD< / a > (< span class = "keywordtype" > unsigned< / span > < span class = "keywordtype" > int< / span > x, < span class = "keywordtype" > unsigned< / span > < span class = "keywordtype" > int< / span > y) {< / div >
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< div class = "line" > < a name = "l00069" > < / a > < span class = "lineno" > 69< / span >   < span class = "keywordflow" > while< / span > (y != 0) {< / div >
< div class = "line" > < a name = "l00070" > < / a > < span class = "lineno" > 70< / span >   < span class = "keywordtype" > unsigned< / span > < span class = "keywordtype" > int< / span > r = x % y;< / div >
< div class = "line" > < a name = "l00071" > < / a > < span class = "lineno" > 71< / span >   x = y;< / div >
< div class = "line" > < a name = "l00072" > < / a > < span class = "lineno" > 72< / span >   y = r;< / div >
< div class = "line" > < a name = "l00073" > < / a > < span class = "lineno" > 73< / span >   }< / div >
< div class = "line" > < a name = "l00074" > < / a > < span class = "lineno" > 74< / span >   < span class = "keywordflow" > return< / span > x;< / div >
< div class = "line" > < a name = "l00075" > < / a > < span class = "lineno" > 75< / span >   }< / div >
< div class = "line" > < a name = "l00076" > < / a > < span class = "lineno" > 76< / span >   < / div >
< div class = "line" > < a name = "l00077" > < / a > < span class = "lineno" > 77< / span >   < span class = "comment" > // Returns the least common multiple of two unsigned integers. Returns zero< / span > < / div >
< div class = "line" > < a name = "l00078" > < / a > < span class = "lineno" > 78< / span >   < span class = "comment" > // if either is zero.< / span > < / div >
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< div class = "line" > < a name = "l00079" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_math_util.html#abbe5e5d1b78a1362e85ed75e3a8f49c5" > 79< / a > < / span >   < span class = "keyword" > static< / span > < span class = "keywordtype" > unsigned< / span > < span class = "keywordtype" > int< / span > < a class = "code" href = "classoperations__research_1_1_math_util.html#abbe5e5d1b78a1362e85ed75e3a8f49c5" > LeastCommonMultiple< / a > (< span class = "keywordtype" > unsigned< / span > < span class = "keywordtype" > int< / span > < a class = "code" href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > , < span class = "keywordtype" > unsigned< / span > < span class = "keywordtype" > int< / span > < a class = "code" href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > ) {< / div >
< div class = "line" > < a name = "l00080" > < / a > < span class = "lineno" > 80< / span >   < span class = "keywordflow" > if< / span > (< a class = "code" href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > > < a class = "code" href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > ) {< / div >
< div class = "line" > < a name = "l00081" > < / a > < span class = "lineno" > 81< / span >   < span class = "keywordflow" > return< / span > (< a class = "code" href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > / < a class = "code" href = "classoperations__research_1_1_math_util.html#a5677e679e0d095f4cfb0a61d213ccdd7" > MathUtil::GCD< / a > (< a class = "code" href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > , < a class = "code" href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > )) * < a class = "code" href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > ;< / div >
< div class = "line" > < a name = "l00082" > < / a > < span class = "lineno" > 82< / span >   } < span class = "keywordflow" > else< / span > < span class = "keywordflow" > if< / span > (< a class = "code" href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > < < a class = "code" href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > ) {< / div >
< div class = "line" > < a name = "l00083" > < / a > < span class = "lineno" > 83< / span >   < span class = "keywordflow" > return< / span > (< a class = "code" href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > / < a class = "code" href = "classoperations__research_1_1_math_util.html#a5677e679e0d095f4cfb0a61d213ccdd7" > MathUtil::GCD< / a > (< a class = "code" href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > , < a class = "code" href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > )) * < a class = "code" href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > ;< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00084" > < / a > < span class = "lineno" > 84< / span >   } < span class = "keywordflow" > else< / span > {< / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00085" > < / a > < span class = "lineno" > 85< / span >   < span class = "keywordflow" > return< / span > < a class = "code" href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > ;< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00086" > < / a > < span class = "lineno" > 86< / span >   }< / div >
< div class = "line" > < a name = "l00087" > < / a > < span class = "lineno" > 87< / span >   }< / div >
< div class = "line" > < a name = "l00088" > < / a > < span class = "lineno" > 88< / span >   < / div >
< div class = "line" > < a name = "l00089" > < / a > < span class = "lineno" > 89< / span >   < span class = "comment" > // Absolute value of x.< / span > < / div >
< div class = "line" > < a name = "l00090" > < / a > < span class = "lineno" > 90< / span >   < span class = "comment" > // Works correctly for unsigned types and< / span > < / div >
< div class = "line" > < a name = "l00091" > < / a > < span class = "lineno" > 91< / span >   < span class = "comment" > // for special floating point values.< / span > < / div >
< div class = "line" > < a name = "l00092" > < / a > < span class = "lineno" > 92< / span >   < span class = "comment" > // Note: 0.0 and -0.0 are not differentiated by Abs (Abs(0.0) is -0.0),< / span > < / div >
< div class = "line" > < a name = "l00093" > < / a > < span class = "lineno" > 93< / span >   < span class = "comment" > // which should be OK: see the comment for Max above.< / span > < / div >
< div class = "line" > < a name = "l00094" > < / a > < span class = "lineno" > 94< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > T> < / div >
2020-10-09 12:00:09 +02:00
< div class = "line" > < a name = "l00095" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_math_util.html#a5a6f14696b2a09c97b58e4f0989b19e7" > 95< / a > < / span >   < span class = "keyword" > static< / span > T < a class = "code" href = "classoperations__research_1_1_math_util.html#a5a6f14696b2a09c97b58e4f0989b19e7" > Abs< / a > (< span class = "keyword" > const< / span > T x) {< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00096" > < / a > < span class = "lineno" > 96< / span >   < span class = "keywordflow" > return< / span > x > 0 ? x : -x;< / div >
< div class = "line" > < a name = "l00097" > < / a > < span class = "lineno" > 97< / span >   }< / div >
< div class = "line" > < a name = "l00098" > < / a > < span class = "lineno" > 98< / span >   < / div >
< div class = "line" > < a name = "l00099" > < / a > < span class = "lineno" > 99< / span >   < span class = "comment" > // Returns the square of x.< / span > < / div >
< div class = "line" > < a name = "l00100" > < / a > < span class = "lineno" > 100< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > T> < / div >
2020-10-09 12:00:09 +02:00
< div class = "line" > < a name = "l00101" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_math_util.html#aac72849250cdf23aefdd991eb0fc0385" > 101< / a > < / span >   < span class = "keyword" > static< / span > T < a class = "code" href = "classoperations__research_1_1_math_util.html#aac72849250cdf23aefdd991eb0fc0385" > Square< / a > (< span class = "keyword" > const< / span > T x) {< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00102" > < / a > < span class = "lineno" > 102< / span >   < span class = "keywordflow" > return< / span > x * x;< / div >
< div class = "line" > < a name = "l00103" > < / a > < span class = "lineno" > 103< / span >   }< / div >
< div class = "line" > < a name = "l00104" > < / a > < span class = "lineno" > 104< / span >   < / div >
< div class = "line" > < a name = "l00105" > < / a > < span class = "lineno" > 105< / span >   < span class = "comment" > // Euclid' s Algorithm.< / span > < / div >
< div class = "line" > < a name = "l00106" > < / a > < span class = "lineno" > 106< / span >   < span class = "comment" > // Returns: the greatest common divisor of two unsigned integers x and y.< / span > < / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00107" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_math_util.html#ae94db7b2fa1d8e1b3c1dc6c683191609" > 107< / a > < / span >   < span class = "keyword" > static< / span > int64_t < a class = "code" href = "classoperations__research_1_1_math_util.html#ae94db7b2fa1d8e1b3c1dc6c683191609" > GCD64< / a > (int64_t x, int64_t y) {< / div >
2020-11-18 14:53:30 +01:00
< div class = "line" > < a name = "l00108" > < / a > < span class = "lineno" > 108< / span >   < a class = "code" href = "base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295" > DCHECK_GE< / a > (x, 0);< / div >
< div class = "line" > < a name = "l00109" > < / a > < span class = "lineno" > 109< / span >   < a class = "code" href = "base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295" > DCHECK_GE< / a > (y, 0);< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00110" > < / a > < span class = "lineno" > 110< / span >   < span class = "keywordflow" > while< / span > (y != 0) {< / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00111" > < / a > < span class = "lineno" > 111< / span >   int64_t r = x % y;< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00112" > < / a > < span class = "lineno" > 112< / span >   x = y;< / div >
< div class = "line" > < a name = "l00113" > < / a > < span class = "lineno" > 113< / span >   y = r;< / div >
< div class = "line" > < a name = "l00114" > < / a > < span class = "lineno" > 114< / span >   }< / div >
< div class = "line" > < a name = "l00115" > < / a > < span class = "lineno" > 115< / span >   < span class = "keywordflow" > return< / span > x;< / div >
< div class = "line" > < a name = "l00116" > < / a > < span class = "lineno" > 116< / span >   }< / div >
< div class = "line" > < a name = "l00117" > < / a > < span class = "lineno" > 117< / span >   < / div >
< div class = "line" > < a name = "l00118" > < / a > < span class = "lineno" > 118< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > T> < / div >
2020-10-09 12:00:09 +02:00
< div class = "line" > < a name = "l00119" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_math_util.html#a622bd31ec5ba0613cc927849af4138ee" > 119< / a > < / span >   < span class = "keyword" > static< / span > T < a class = "code" href = "classoperations__research_1_1_math_util.html#a622bd31ec5ba0613cc927849af4138ee" > IPow< / a > (T base, < span class = "keywordtype" > int< / span > exp) {< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00120" > < / a > < span class = "lineno" > 120< / span >   < span class = "keywordflow" > return< / span > pow(base, exp);< / div >
< div class = "line" > < a name = "l00121" > < / a > < span class = "lineno" > 121< / span >   }< / div >
< div class = "line" > < a name = "l00122" > < / a > < span class = "lineno" > 122< / span >   < / div >
< div class = "line" > < a name = "l00123" > < / a > < span class = "lineno" > 123< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > class< / span > IntOut, < span class = "keyword" > class< / span > FloatIn> < / div >
2020-10-09 12:00:09 +02:00
< div class = "line" > < a name = "l00124" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_math_util.html#aad6225dda2c124a0e6acdc496d306f41" > 124< / a > < / span >   < span class = "keyword" > static< / span > IntOut < a class = "code" href = "classoperations__research_1_1_math_util.html#aad6225dda2c124a0e6acdc496d306f41" > Round< / a > (FloatIn x) {< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00125" > < / a > < span class = "lineno" > 125< / span >   < span class = "comment" > // We don' t use sgn(x) below because there is no need to distinguish the< / span > < / div >
< div class = "line" > < a name = "l00126" > < / a > < span class = "lineno" > 126< / span >   < span class = "comment" > // (x == 0) case. Also note that there are specialized faster versions< / span > < / div >
< div class = "line" > < a name = "l00127" > < / a > < span class = "lineno" > 127< / span >   < span class = "comment" > // of this function for Intel, ARM and PPC processors at the bottom< / span > < / div >
< div class = "line" > < a name = "l00128" > < / a > < span class = "lineno" > 128< / span >   < span class = "comment" > // of this file.< / span > < / div >
< div class = "line" > < a name = "l00129" > < / a > < span class = "lineno" > 129< / span >   < span class = "keywordflow" > if< / span > (x > -0.5 & & x < 0.5) {< / div >
< div class = "line" > < a name = "l00130" > < / a > < span class = "lineno" > 130< / span >   < span class = "comment" > // This case is special, because for largest floating point number< / span > < / div >
< div class = "line" > < a name = "l00131" > < / a > < span class = "lineno" > 131< / span >   < span class = "comment" > // below 0.5, the addition of 0.5 yields 1 and this would lead< / span > < / div >
< div class = "line" > < a name = "l00132" > < / a > < span class = "lineno" > 132< / span >   < span class = "comment" > // to incorrect result.< / span > < / div >
< div class = "line" > < a name = "l00133" > < / a > < span class = "lineno" > 133< / span >   < span class = "keywordflow" > return< / span > < span class = "keyword" > static_cast< < / span > IntOut< span class = "keyword" > > < / span > (0);< / div >
< div class = "line" > < a name = "l00134" > < / a > < span class = "lineno" > 134< / span >   }< / div >
< div class = "line" > < a name = "l00135" > < / a > < span class = "lineno" > 135< / span >   < span class = "keywordflow" > return< / span > < span class = "keyword" > static_cast< < / span > IntOut< span class = "keyword" > > < / span > (x < 0 ? (x - 0.5) : (x + 0.5));< / div >
< div class = "line" > < a name = "l00136" > < / a > < span class = "lineno" > 136< / span >   }< / div >
< div class = "line" > < a name = "l00137" > < / a > < span class = "lineno" > 137< / span >   < / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00138" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_math_util.html#a55fc8a3af7c2526c83e83586cd578d89" > 138< / a > < / span >   < span class = "keyword" > static< / span > int64_t < a class = "code" href = "classoperations__research_1_1_math_util.html#a55fc8a3af7c2526c83e83586cd578d89" > FastInt64Round< / a > (< span class = "keywordtype" > double< / span > x) { < span class = "keywordflow" > return< / span > Round< int64_t> (x); }< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00139" > < / a > < span class = "lineno" > 139< / span >   };< / div >
< div class = "line" > < a name = "l00140" > < / a > < span class = "lineno" > 140< / span >   } < span class = "comment" > // namespace operations_research< / span > < / div >
< div class = "line" > < a name = "l00141" > < / a > < span class = "lineno" > 141< / span >   < / div >
2021-01-26 11:28:50 +01:00
< div class = "line" > < a name = "l00142" > < / a > < span class = "lineno" > 142< / span >   < span class = "preprocessor" > #endif < / span > < span class = "comment" > // OR_TOOLS_BASE_MATHUTIL_H_< / span > < / div >
2020-09-02 09:42:51 +02:00
< div class = "ttc" id = "abase_2logging_8h_html" > < div class = "ttname" > < a href = "base_2logging_8h.html" > logging.h< / a > < / div > < / div >
2021-04-27 23:00:03 +02:00
< div class = "ttc" id = "abase_2logging_8h_html_a46e69120fbd3b36e6960e096d23b66f0" > < div class = "ttname" > < a href = "base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0" > DCHECK_NE< / a > < / div > < div class = "ttdeci" > #define DCHECK_NE(val1, val2)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "base_2logging_8h_source.html#l00894" > base/logging.h:894< / a > < / div > < / div >
< div class = "ttc" id = "abase_2logging_8h_html_aae2dc65d9ea248d54bf39daa986dd295" > < div class = "ttname" > < a href = "base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295" > DCHECK_GE< / a > < / div > < div class = "ttdeci" > #define DCHECK_GE(val1, val2)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "base_2logging_8h_source.html#l00897" > base/logging.h:897< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "abasictypes_8h_html" > < div class = "ttname" > < a href = "basictypes_8h.html" > basictypes.h< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1_math_util_html" > < div class = "ttname" > < a href = "classoperations__research_1_1_math_util.html" > operations_research::MathUtil< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "mathutil_8h_source.html#l00029" > mathutil.h:29< / a > < / div > < / div >
2020-10-09 12:00:09 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1_math_util_html_a0cfaf8b139304c54e3403d4ffbd60157" > < div class = "ttname" > < a href = "classoperations__research_1_1_math_util.html#a0cfaf8b139304c54e3403d4ffbd60157" > operations_research::MathUtil::CeilOfRatio< / a > < / div > < div class = "ttdeci" > static IntegralType CeilOfRatio(IntegralType numerator, IntegralType denominator)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "mathutil_8h_source.html#l00039" > mathutil.h:39< / a > < / div > < / div >
2021-04-27 23:00:03 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1_math_util_html_a55fc8a3af7c2526c83e83586cd578d89" > < div class = "ttname" > < a href = "classoperations__research_1_1_math_util.html#a55fc8a3af7c2526c83e83586cd578d89" > operations_research::MathUtil::FastInt64Round< / a > < / div > < div class = "ttdeci" > static int64_t FastInt64Round(double x)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "mathutil_8h_source.html#l00138" > mathutil.h:138< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1_math_util_html_a5677e679e0d095f4cfb0a61d213ccdd7" > < div class = "ttname" > < a href = "classoperations__research_1_1_math_util.html#a5677e679e0d095f4cfb0a61d213ccdd7" > operations_research::MathUtil::GCD< / a > < / div > < div class = "ttdeci" > static unsigned int GCD(unsigned int x, unsigned int y)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "mathutil_8h_source.html#l00068" > mathutil.h:68< / a > < / div > < / div >
2020-10-09 12:00:09 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1_math_util_html_a5a6f14696b2a09c97b58e4f0989b19e7" > < div class = "ttname" > < a href = "classoperations__research_1_1_math_util.html#a5a6f14696b2a09c97b58e4f0989b19e7" > operations_research::MathUtil::Abs< / a > < / div > < div class = "ttdeci" > static T Abs(const T x)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "mathutil_8h_source.html#l00095" > mathutil.h:95< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1_math_util_html_a622bd31ec5ba0613cc927849af4138ee" > < div class = "ttname" > < a href = "classoperations__research_1_1_math_util.html#a622bd31ec5ba0613cc927849af4138ee" > operations_research::MathUtil::IPow< / a > < / div > < div class = "ttdeci" > static T IPow(T base, int exp)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "mathutil_8h_source.html#l00119" > mathutil.h:119< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1_math_util_html_a9e5c13b72c36481ed098c05031d1f850" > < div class = "ttname" > < a href = "classoperations__research_1_1_math_util.html#a9e5c13b72c36481ed098c05031d1f850" > operations_research::MathUtil::FloorOfRatio< / a > < / div > < div class = "ttdeci" > static IntegralType FloorOfRatio(IntegralType numerator, IntegralType denominator)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "mathutil_8h_source.html#l00053" > mathutil.h:53< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1_math_util_html_aac72849250cdf23aefdd991eb0fc0385" > < div class = "ttname" > < a href = "classoperations__research_1_1_math_util.html#aac72849250cdf23aefdd991eb0fc0385" > operations_research::MathUtil::Square< / a > < / div > < div class = "ttdeci" > static T Square(const T x)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "mathutil_8h_source.html#l00101" > mathutil.h:101< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1_math_util_html_aad6225dda2c124a0e6acdc496d306f41" > < div class = "ttname" > < a href = "classoperations__research_1_1_math_util.html#aad6225dda2c124a0e6acdc496d306f41" > operations_research::MathUtil::Round< / a > < / div > < div class = "ttdeci" > static IntOut Round(FloatIn x)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "mathutil_8h_source.html#l00124" > mathutil.h:124< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1_math_util_html_abbe5e5d1b78a1362e85ed75e3a8f49c5" > < div class = "ttname" > < a href = "classoperations__research_1_1_math_util.html#abbe5e5d1b78a1362e85ed75e3a8f49c5" > operations_research::MathUtil::LeastCommonMultiple< / a > < / div > < div class = "ttdeci" > static unsigned int LeastCommonMultiple(unsigned int a, unsigned int b)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "mathutil_8h_source.html#l00079" > mathutil.h:79< / a > < / div > < / div >
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< div class = "ttc" id = "aclassoperations__research_1_1_math_util_html_ae94db7b2fa1d8e1b3c1dc6c683191609" > < div class = "ttname" > < a href = "classoperations__research_1_1_math_util.html#ae94db7b2fa1d8e1b3c1dc6c683191609" > operations_research::MathUtil::GCD64< / a > < / div > < div class = "ttdeci" > static int64_t GCD64(int64_t x, int64_t y)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "mathutil_8h_source.html#l00107" > mathutil.h:107< / 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 >
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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" > < 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 >
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