OMCompiler/Compiler/Util/Rational.mo
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| 1 | /* | ||
| 2 | * This file is part of OpenModelica. | ||
| 3 | * | ||
| 4 | * Copyright (c) 1998-2026, Open Source Modelica Consortium (OSMC), | ||
| 5 | * c/o Linköpings universitet, Department of Computer and Information Science, | ||
| 6 | * SE-58183 Linköping, Sweden. | ||
| 7 | * | ||
| 8 | * All rights reserved. | ||
| 9 | * | ||
| 10 | * THIS PROGRAM IS PROVIDED UNDER THE TERMS OF AGPL VERSION 3 LICENSE OR | ||
| 11 | * THIS OSMC PUBLIC LICENSE (OSMC-PL) VERSION 1.8. | ||
| 12 | * ANY USE, REPRODUCTION OR DISTRIBUTION OF THIS PROGRAM CONSTITUTES | ||
| 13 | * RECIPIENT'S ACCEPTANCE OF THE OSMC PUBLIC LICENSE OR THE GNU AGPL | ||
| 14 | * VERSION 3, ACCORDING TO RECIPIENTS CHOICE. | ||
| 15 | * | ||
| 16 | * The OpenModelica software and the OSMC (Open Source Modelica Consortium) | ||
| 17 | * Public License (OSMC-PL) are obtained from OSMC, either from the above | ||
| 18 | * address, from the URLs: | ||
| 19 | * http://www.openmodelica.org or | ||
| 20 | * https://github.com/OpenModelica/ or | ||
| 21 | * http://www.ida.liu.se/projects/OpenModelica, | ||
| 22 | * and in the OpenModelica distribution. | ||
| 23 | * | ||
| 24 | * GNU AGPL version 3 is obtained from: | ||
| 25 | * https://www.gnu.org/licenses/licenses.html#GPL | ||
| 26 | * | ||
| 27 | * This program is distributed WITHOUT ANY WARRANTY; without | ||
| 28 | * even the implied warranty of MERCHANTABILITY or FITNESS | ||
| 29 | * FOR A PARTICULAR PURPOSE, EXCEPT AS EXPRESSLY SET FORTH | ||
| 30 | * IN THE BY RECIPIENT SELECTED SUBSIDIARY LICENSE CONDITIONS OF OSMC-PL. | ||
| 31 | * | ||
| 32 | * See the full OSMC Public License conditions for more details. | ||
| 33 | * | ||
| 34 | */ | ||
| 35 | |||
| 36 | encapsulated uniontype Rational | ||
| 37 | |||
| 38 | protected | ||
| 39 | import Util; | ||
| 40 | |||
| 41 | public | ||
| 42 | record RATIONAL | ||
| 43 | Integer n "numerator"; | ||
| 44 | Integer d "denominator"; | ||
| 45 | end RATIONAL; | ||
| 46 | |||
| 47 | constant Rational ZERO = RATIONAL(0, 1); | ||
| 48 | constant Rational ONE = RATIONAL(1, 1); | ||
| 49 | |||
| 50 | function isEqual | ||
| 51 | input Rational r1; | ||
| 52 | input Rational r2; | ||
| 53 | output Boolean b = r1.n == r2.n and r1.d == r2.d; | ||
| 54 | end isEqual; | ||
| 55 | |||
| 56 | function compare "Compares two rationals and return -1 if the first is smallest, 1 if the second is smallest, or 0 if they are equal." | ||
| 57 | input Rational r1; | ||
| 58 | input Rational r2; | ||
| 59 | output Integer i; | ||
| 60 | protected | ||
| 61 | // Divide by common divisors to avoid overflow | ||
| 62 | Integer gn = Util.gcd(r1.n, r2.n); | ||
| 63 | Integer gd = Util.gcd(r1.d, r2.d); | ||
| 64 | algorithm | ||
| 65 | ✗ | i := Util.intCompare(intDiv(r1.n, gn)*intDiv(r2.d, gd), intDiv(r2.n, gn)*intDiv(r1.d, gd)); | |
| 66 | end compare; | ||
| 67 | |||
| 68 | function toString | ||
| 69 | input Rational r; | ||
| 70 | output String str = intString(r.n) + "/" + intString(r.d); | ||
| 71 | end toString; | ||
| 72 | |||
| 73 | function normalize | ||
| 74 | input output Rational r; | ||
| 75 | algorithm | ||
| 76 |
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54 | if r.n == 0 then |
| 77 | 26 | r.d := 1; | |
| 78 | elseif r.d < 0 then | ||
| 79 | ✗ | r := RATIONAL(-r.n, -r.d); | |
| 80 | end if; | ||
| 81 | end normalize; | ||
| 82 | |||
| 83 | function add "a/b + c/d = (ad + bc)/(bd) = (a(d/g) + (b/g)c)/((b/g)d)" | ||
| 84 | input Rational r1; | ||
| 85 | input Rational r2; | ||
| 86 | output Rational r; | ||
| 87 | protected | ||
| 88 | Integer g = Util.gcd(r1.d, r2.d); | ||
| 89 | algorithm | ||
| 90 |
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18 | r := reduce(r1.n*intDiv(r2.d, g) + intDiv(r1.d, g)*r2.n, intDiv(r1.d,g)*r2.d); |
| 91 | end add; | ||
| 92 | |||
| 93 | function neg "-(a/b) = (-a)/b" | ||
| 94 | input Rational r; | ||
| 95 | output Rational s = RATIONAL(-r.n, r.d); | ||
| 96 | end neg; | ||
| 97 | |||
| 98 | function sub "a/b - c/d = (ad - bc)/(bd) = (a(d/g) - (b/g)c)/((b/g)d)" | ||
| 99 | input Rational r1; | ||
| 100 | input Rational r2; | ||
| 101 | output Rational r; | ||
| 102 | protected | ||
| 103 | Integer g = Util.gcd(r1.d, r2.d); | ||
| 104 | algorithm | ||
| 105 | ✗ | r := reduce(r1.n*intDiv(r2.d, g) - intDiv(r1.d, g)*r2.n, intDiv(r1.d,g)*r2.d); | |
| 106 | end sub; | ||
| 107 | |||
| 108 | function mul "a/b * c/d = (ac)/(bd) = ((a/g1)(c/g2))/((b/g2)(d/g1))" | ||
| 109 | input Rational r1; | ||
| 110 | input Rational r2; | ||
| 111 | output Rational r; | ||
| 112 | protected | ||
| 113 | Integer g1 = Util.gcd(r1.n, r2.d); | ||
| 114 | Integer g2 = Util.gcd(r2.n, r1.d); | ||
| 115 | algorithm | ||
| 116 |
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36 | r := reduce(intDiv(r1.n, g1)*intDiv(r2.n, g2), intDiv(r1.d, g2)*intDiv(r2.d, g1)); |
| 117 | end mul; | ||
| 118 | |||
| 119 | function inv "(a/b)^(-1) = b/a" | ||
| 120 | input Rational r; | ||
| 121 | output Rational s = RATIONAL(Util.intSign(r.n)*r.d, intAbs(r.n)); | ||
| 122 | end inv; | ||
| 123 | |||
| 124 | function div "(a/b) / (c/d) = (ad)/(bc) = ((a/g1)(d/g2))/((b/g2)(c/g1))" | ||
| 125 | input Rational r1; | ||
| 126 | input Rational r2; | ||
| 127 | output Rational r; | ||
| 128 | protected | ||
| 129 | Integer g1 = Util.gcd(r1.n, r2.n); | ||
| 130 | Integer g2 = Util.gcd(r2.d, r1.d); | ||
| 131 | algorithm | ||
| 132 | ✗ | r := reduce(intDiv(r1.n, g1)*intDiv(r2.d, g2), intDiv(r1.d, g2)*intDiv(r2.n, g1)); | |
| 133 | end div; | ||
| 134 | |||
| 135 | protected | ||
| 136 | function reduce | ||
| 137 | input Integer i1; | ||
| 138 | input Integer i2; | ||
| 139 | output Rational r; | ||
| 140 | protected | ||
| 141 | Integer d = Util.gcd(i1, i2); | ||
| 142 | algorithm | ||
| 143 |
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54 | r := normalize(RATIONAL(intDiv(i1, d), intDiv(i2, d))); |
| 144 | end reduce; | ||
| 145 | annotation(__OpenModelica_Interface="util"); | ||
| 146 | end Rational; | ||
| 147 |