List of usage examples for org.apache.commons.math3.util ArithmeticUtils lcm
public static long lcm(long a, long b) throws MathArithmeticException
Returns the least common multiple of the absolute value of two numbers, using the formula lcm(a,b) = (a / gcd(a,b)) * b .
From source file:com.udojava.evalex.Expression.java
/** * Creates a new expression instance from an expression string with a given * default match context./*from w ww . j av a 2 s . c o m*/ * * @param expression The expression. E.g. <code>"2.4*sin(3)/(2-4)"</code> or * <code>"sin(y)>0 & max(z, 3)>3"</code> */ public Expression(String expression, LinkedList<String> hist, Variables vars) { this.history = hist; this.expression = expression; mainVars = vars; addOperator(new Operator("+", 20, true, "Addition") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { if (v1.type == ValueType.ARRAY) { MyComplex vo = new MyComplex(v1.list); vo.list.add(v2); return vo; } return v1.add(v2); } }); addOperator(new Operator("-", 20, true, "Subtraction") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { if (v1.type == ValueType.ARRAY) { MyComplex vo = new MyComplex(v1.list); vo.list.removeIf(o -> o.equals(v2)); return vo; } return v1.subtract(v2); } }); addOperator(new Operator("*", 30, true, "Real number multiplication") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { return v1.multiply(v2); } }); addOperator(new Operator("/", 30, true, "Real number division") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { return v1.divide(v2); } }); addOperator(new Operator("%", 30, true, "Remainder of integer division") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { double r = v1.real % v2.real; return new MyComplex(r); } }); addOperator( new Operator("^", 40, false, "Exponentation. See: https://en.wikipedia.org/wiki/Exponentiation") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { return v1.pow(v2); } }); addOperator(new Operator("&&", 4, false, "Logical AND. Evaluates to 1 if both operands are not 0") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { boolean b1 = (v1.real == 0.0 && v2.real == 0.0); return new MyComplex(b1 ? 1 : 0); } }); addOperator(new Operator("||", 2, false, "Logical OR. Evaluates to 0 if both operands are 0") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { boolean b1 = (v1.real == 0.0 && v2.real == 0.0); return new MyComplex(b1 ? 0 : 1); } }); addOperator(new Operator(">", 10, false, "Greater than. See: See: https://en.wikipedia.org/wiki/Inequality_(mathematics)") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { if (v1.type == ValueType.REAL && v2.type == ValueType.REAL) { return new MyComplex(v1.real > v2.real ? 1 : 0); } else { return new MyComplex(v1.abs() > v2.abs() ? 1 : 0); } } }); addOperator(new Operator(">=", 10, false, "Greater or equal") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { if (v1.type == ValueType.REAL && v2.type == ValueType.REAL) { return new MyComplex(v1.real >= v2.real ? 1 : 0); } else { return new MyComplex(v1.abs() >= v2.abs() ? 1 : 0); } } }); addOperator(new Operator("<", 10, false, "Less than. See: https://en.wikipedia.org/wiki/Inequality_(mathematics)") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { if (v1.type == ValueType.REAL && v2.type == ValueType.REAL) { return new MyComplex(v1.real < v2.real ? 1 : 0); } else { return new MyComplex(v1.abs() < v2.abs() ? 1 : 0); } } }); addOperator(new Operator("<=", 10, false, "less or equal") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { if (v1.type == ValueType.REAL && v2.type == ValueType.REAL) { return new MyComplex(v1.real <= v2.real ? 1 : 0); } else { return new MyComplex(v1.abs() <= v2.abs() ? 1 : 0); } } }); addOperator(new Operator("->", 7, false, "Set variable v to new value ") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { if (v1 instanceof PitDecimal) { PitDecimal target = (PitDecimal) v1; String s = target.getVarToken(); setVariable(s, v2); return v2; } throw new ExpressionException("LHS not variable"); } }); addOperator(new Operator("=", 7, false, "Equality") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { if (v1.type == ValueType.REAL && v2.type == ValueType.REAL) { return new MyComplex(v1.real == v2.real ? 1 : 0); } else { return new MyComplex(v1.abs() == v2.abs() ? 1 : 0); } } }); addOperator(new Operator("!=", 7, false, "Inequality. See: https://en.wikipedia.org/wiki/Inequality_(mathematics)") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { if (v1.type == ValueType.REAL && v2.type == ValueType.REAL) { return new MyComplex(v1.real != v2.real ? 1 : 0); } else { return new MyComplex(v1.abs() != v2.abs() ? 1 : 0); } } }); addOperator( new Operator("or", 7, false, "Bitwise OR. See: https://en.wikipedia.org/wiki/Logical_disjunction") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { return new MyComplex((long) v1.real | (long) v2.real); } }); addOperator(new Operator("and", 7, false, "Bitwise AND. See: https://en.wikipedia.org/wiki/Logical_conjunction") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { return new MyComplex((long) v1.real & (long) v2.real); } }); addOperator(new Operator("xor", 7, false, "Bitwise XOR, See: https://en.wikipedia.org/wiki/Exclusive_or") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { return new MyComplex((long) v1.real ^ (long) v2.real); } }); addOperator(new Operator("!", 50, true, "Factorial. See https://en.wikipedia.org/wiki/Factorial") { public BigInteger factorial(long n) { BigInteger factorial = BigInteger.ONE; for (long i = 1; i <= n; i++) { factorial = factorial.multiply(BigInteger.valueOf(i)); } return factorial; } @Override public MyComplex eval(MyComplex v1, MyComplex v2) { BigInteger fact = factorial((long) v1.real); return new MyComplex(fact, BigInteger.ZERO); } }); addOperator(new Operator("~", 8, false, "Bitwise negation") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { BigInteger bi = v2.toBigIntegerReal(); int c = bi.bitLength(); if (c == 0) { return new MyComplex(1); } for (int s = 0; s < c; s++) { bi = bi.flipBit(s); } return new MyComplex(bi); } }); addOperator(new Operator("shl", 8, false, "Left Bit shift") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { return new MyComplex((long) v1.real << (long) v2.real); } }); addOperator(new Operator("shr", 8, false, "Right bit shift") { @Override public MyComplex eval(MyComplex v1, MyComplex v2) { return new MyComplex((long) v1.real >>> (long) v2.real); } }); addFunction(new Function("NOT", 1, "evaluates to 0 if argument != 0") { @Override public MyComplex eval(List<MyComplex> parameters) { boolean zero = parameters.get(0).abs() == 0; return new MyComplex(zero ? 1 : 0); } }); addFunction(new Function("RND", 2, "Give random number in the range between first and second argument") { @Override public MyComplex eval(List<MyComplex> parameters) { double low = parameters.get(0).real; double high = parameters.get(1).real; return new MyComplex(low + Math.random() * (high - low)); } }); MersenneTwister mers = new MersenneTwister(System.nanoTime()); addFunction(new Function("MRS", 0, "Mersenne twister random generator") { @Override public MyComplex eval(List<MyComplex> parameters) { return new MyComplex(mers.nextDouble()); } }); addFunction(new Function("BIN", 2, "Binomial Coefficient 'n choose k'") { @Override public MyComplex eval(List<MyComplex> parameters) { int n = (int) parameters.get(0).real; int k = (int) parameters.get(1).real; double d = CombinatoricsUtils.binomialCoefficientDouble(n, k); return new MyComplex(d); } }); addFunction(new Function("STIR", 2, "Stirling number of 2nd kind: http://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html") { @Override public MyComplex eval(List<MyComplex> parameters) { int n = (int) parameters.get(0).real; int k = (int) parameters.get(1).real; double d = CombinatoricsUtils.stirlingS2(n, k); return new MyComplex(d); } }); addFunction(new Function("SIN", 1, "Sine function") { @Override public MyComplex eval(List<MyComplex> parameters) { return parameters.get(0).sin(); } }); addFunction(new Function("COS", 1, "Cosine function") { @Override public MyComplex eval(List<MyComplex> parameters) { return parameters.get(0).cos(); } }); addFunction(new Function("TAN", 1, "Tangent") { @Override public MyComplex eval(List<MyComplex> parameters) { return parameters.get(0).tan(); } }); addFunction(new Function("ASIN", 1, "Reverse Sine") { // added by av @Override public MyComplex eval(List<MyComplex> parameters) { return parameters.get(0).asin(); } }); addFunction(new Function("ACOS", 1, "Reverse Cosine") { // added by av @Override public MyComplex eval(List<MyComplex> parameters) { return parameters.get(0).acos(); } }); addFunction(new Function("ATAN", 1, "Reverse Tangent") { // added by av @Override public MyComplex eval(List<MyComplex> parameters) { return parameters.get(0).atan(); } }); addFunction(new Function("SINH", 1, "Hyperbolic Sine") { @Override public MyComplex eval(List<MyComplex> parameters) { return parameters.get(0).sinh(); } }); addFunction(new Function("COSH", 1, "Hyperbolic Cosine") { @Override public MyComplex eval(List<MyComplex> parameters) { return parameters.get(0).cosh(); } }); addFunction(new Function("TANH", 1, "Hyperbolic Tangent") { @Override public MyComplex eval(List<MyComplex> parameters) { return parameters.get(0).tanh(); } }); addFunction(new Function("RAD", 1, "Transform degree to radian") { @Override public MyComplex eval(List<MyComplex> parameters) { double d = Math.toRadians(parameters.get(0).real); return new MyComplex(d); } }); addFunction(new Function("DEG", 1, "Transform radian to degree") { @Override public MyComplex eval(List<MyComplex> parameters) { double d = Math.toDegrees(parameters.get(0).real); return new MyComplex(d); } }); addFunction(new Function("MAX", -1, "Find the biggest value in a list") { @Override public MyComplex eval(List<MyComplex> parameters) { MyComplex save = new MyComplex(Double.MIN_VALUE); if (parameters.size() == 0) { throw new ExpressionException("MAX requires at least one parameter"); } // if (parameters.get(0).type == ValueType.ARRAY) // parameters = parameters.get(0).list; if (parameters.get(0).type == ValueType.COMPLEX) { for (MyComplex parameter : parameters) { if (parameter.abs() > save.abs()) { save = parameter; } } save.type = ValueType.COMPLEX; } else { for (MyComplex parameter : parameters) { if (parameter.real > save.real) { save = parameter; } } save.type = ValueType.REAL; } return save; } }); /////////////////////////////////////////////////////// addFunction(new Function("IF", 3, "Conditional: give param3 if param1 is 0, otherwise param2") { @Override public MyComplex eval(List<MyComplex> parameters) { if (parameters.get(0).real == 0.0) { return parameters.get(2); } return parameters.get(1); } }); addFunction(new Function("PERC", 2, "Get param1 percent of param2") { @Override public MyComplex eval(List<MyComplex> parameters) { return parameters.get(0).divide(new MyComplex(100)).multiply(parameters.get(1)); } }); addFunction(new Function("PER", 2, "How many percent is param1 of param2") { @Override public MyComplex eval(List<MyComplex> parameters) { return parameters.get(0).multiply(new MyComplex(100)).divide(parameters.get(1)); } }); addFunction(new Function("H", 1, "Evaluate _history element") { @Override public MyComplex eval(List<MyComplex> parameters) { int i = (int) parameters.get(0).real; Expression ex = new Expression(history.get(i), history, mainVars); return ex.eval(); } }); addFunction(new Function("MERS", 1, "Calculate Mersenne Number") { @Override public MyComplex eval(List<MyComplex> parameters) { MyComplex p = parameters.get(0); return new MyComplex(2).pow(p).subtract(new MyComplex(1)); } }); addFunction(new Function("GCD", 2, "Find greatest common divisor of 2 values") { @Override public MyComplex eval(List<MyComplex> parameters) { double a = parameters.get(0).real; double b = parameters.get(1).real; long r = ArithmeticUtils.gcd((long) a, (long) b); return new MyComplex(r); } }); addFunction(new Function("LCM", 2, "Find least common multiple of 2 values") { @Override public MyComplex eval(List<MyComplex> parameters) { double a = parameters.get(0).real; double b = parameters.get(1).real; long r = ArithmeticUtils.lcm((long) a, (long) b); return new MyComplex(r); } }); addFunction(new Function("AMEAN", -1, "Arithmetic mean of a set of values") { @Override public MyComplex eval(List<MyComplex> parameters) { if (parameters.size() == 0) { throw new ExpressionException("MEAN requires at least one parameter"); } Mean m = new Mean(); double[] d = MyComplex.getRealArray(parameters); double d2 = m.evaluate(d); return new MyComplex(d2); } }); // addFunction(new Function("BYT", -1, // "Value from sequence of bytes") // { // @Override // public MyComplex eval (List<MyComplex> parameters) // { // if (parameters.size() == 0) // { // return MyComplex.ZERO; // } // BigInteger res = BigInteger.ZERO; // for (MyComplex parameter : parameters) // { // if (parameter.intValue() < 0 || parameter.intValue() > 255) // { // throw new ExpressionException("not a byte value"); // } // res = res.shiftLeft(8); // res = res.or(parameter.toBigInteger()); // } // return new MyComplex(res, BigInteger.ZERO); // } // }); addFunction(new Function("SEQ", 3, "Generate Sequence p1=start, p2=step, p3=count") { @Override public MyComplex eval(List<MyComplex> parameters) { double start = parameters.get(0).real; ArrayList<MyComplex> arr = new ArrayList<>(); for (int s = 0; s < (int) (parameters.get(2).real); s++) { arr.add(new MyComplex(start)); start += parameters.get(1).real; } return new MyComplex(arr); } }); addFunction(new Function("PROD", -1, "Product of real values") { @Override public MyComplex eval(List<MyComplex> parameters) { Product p = new Product(); double[] d = MyComplex.getRealArray(parameters); return new MyComplex(p.evaluate(d)); } }); addFunction(new Function("SUM", -1, "Sum of values") { @Override public MyComplex eval(List<MyComplex> parameters) { Sum p = new Sum(); double[] d = MyComplex.getRealArray(parameters); return new MyComplex(p.evaluate(d)); } }); addFunction(new Function("ANG", 1, "Angle phi of complex number in radians") { @Override public MyComplex eval(List<MyComplex> parameters) { double b = parameters.get(0).angle(); return new MyComplex(b); } }); addFunction(new Function("IM", 1, "Get imaginary part") { @Override public MyComplex eval(List<MyComplex> parameters) { return new MyComplex(parameters.get(0).imaginary); } }); addFunction(new Function("RE", 1, "Get real part") { @Override public MyComplex eval(List<MyComplex> parameters) { return new MyComplex(parameters.get(0).real); } }); addFunction(new Function("POL", 2, "Make complex number from polar coords. angle is first arg") { @Override public MyComplex eval(List<MyComplex> parameters) { double angle = parameters.get(0).real; double len = parameters.get(1).real; Complex c = ComplexUtils.polar2Complex(len, angle); return new MyComplex(c); } }); addFunction(new Function("GMEAN", -1, "Geometric mean of a set of values") { @Override public MyComplex eval(List<MyComplex> parameters) { if (parameters.size() == 0) { throw new ExpressionException("MEAN requires at least one parameter"); } GeometricMean m = new GeometricMean(); double[] d = MyComplex.getRealArray(parameters); double d2 = m.evaluate(d); return new MyComplex(d2); } }); addFunction(new Function("HMEAN", -1, "Harmonic mean of a set of values") { @Override public MyComplex eval(List<MyComplex> parameters) { if (parameters.size() == 0) { throw new ExpressionException("MEAN requires at least one parameter"); } MyComplex res = new MyComplex(0); int num = 0; for (MyComplex parameter : parameters) { res = res.add(new MyComplex(1).divide(parameter)); num++; } res = new MyComplex(res.abs()); return new MyComplex(num).divide(res); } }); addFunction(new Function("VAR", -1, "Variance of a set of values") { @Override public MyComplex eval(List<MyComplex> parameters) { if (parameters.size() == 0) { throw new ExpressionException("MEAN requires at least one parameter"); } double[] arr = new double[parameters.size()]; for (int s = 0; s < parameters.size(); s++) { arr[s] = parameters.get(s).real; } return new MyComplex(variance(arr)); } }); addFunction(new Function("NPR", 1, "Next prime number greater or equal the argument") { @Override public MyComplex eval(List<MyComplex> parameters) { return new MyComplex(nextPrime((int) parameters.get(0).real)); } }); addFunction(new Function("NSWP", 1, "Swap nibbles") { @Override public MyComplex eval(List<MyComplex> parameters) { BigInteger bi = parameters.get(0).toBigIntegerReal(); String s = bi.toString(16); s = new StringBuilder(s).reverse().toString(); return new MyComplex(new BigInteger(s, 16), BigInteger.ZERO); } }); addFunction(new Function("BSWP", 1, "Swap bytes") { @Override public MyComplex eval(List<MyComplex> parameters) { BigInteger bi = parameters.get(0).toBigIntegerReal(); String s = bi.toString(16); while (s.length() % 4 != 0) { s = s + "0"; } if (bi.intValue() < 256) { s = "00" + s; } s = Misc.reverseHex(s); return new MyComplex(new BigInteger(s, 16), BigInteger.ZERO); } }); addFunction(new Function("PYT", 2, "Pythagoras's result = sqrt(param1^2+param2^2) https://en.wikipedia.org/wiki/Pythagorean_theorem") { @Override public MyComplex eval(List<MyComplex> par) { double a = par.get(0).real; double b = par.get(1).real; return new MyComplex(Math.sqrt(a * a + b * b)); } }); addFunction(new Function("FIB", 1, "Fibonacci number") { // --Commented out by Inspection (2/19/2017 7:46 PM):private final Operator exp = operators.get("^"); @Override public MyComplex eval(List<MyComplex> par) { return Misc.iterativeFibonacci((int) par.get(0).real); } }); /////////////////////////////////////////////// addFunction(new Function("MIN", -1, "Find the smallest in a list of values") { @Override public MyComplex eval(List<MyComplex> parameters) { MyComplex save = new MyComplex(Double.MAX_VALUE); if (parameters.size() == 0) { throw new ExpressionException("MAX requires at least one parameter"); } if (parameters.get(0).type == ValueType.COMPLEX) { for (MyComplex parameter : parameters) { if (parameter.abs() < save.abs()) { save = parameter; } } save.type = ValueType.COMPLEX; } else { for (MyComplex parameter : parameters) { if (parameter.real < save.real) { save = parameter; } } save.type = ValueType.REAL; } return save; } }); addFunction(new Function("ABS", 1, "Get absolute value of a number") { @Override public MyComplex eval(List<MyComplex> parameters) { return new MyComplex(parameters.get(0).abs()); } }); addFunction(new Function("LN", 1, "Logarithm base e of the argument") { @Override public MyComplex eval(List<MyComplex> parameters) { double d = Math.log(parameters.get(0).real); return new MyComplex(d); } }); addFunction(new Function("LOG", 1, "Logarithm base 10 of the argument") { @Override public MyComplex eval(List<MyComplex> parameters) { double d = Math.log10(parameters.get(0).real); return new MyComplex(d); } }); addFunction(new Function("FLOOR", 1, "Rounds DOWN to nearest Integer") { @Override public MyComplex eval(List<MyComplex> parameters) { double d = Math.floor(parameters.get(0).real); return new MyComplex(d); } }); addFunction(new Function("CEIL", 1, "Rounds UP to nearest Integer") { @Override public MyComplex eval(List<MyComplex> parameters) { double d = Math.ceil(parameters.get(0).real); return new MyComplex(d); } }); addFunction(new Function("ROU", 1, "Rounds to nearest Integer") { @Override public MyComplex eval(List<MyComplex> parameters) { int d = (int) (parameters.get(0).real + 0.5); return new MyComplex(d); } }); addFunction(new Function("SQRT", 1, "Square root") { @Override public MyComplex eval(List<MyComplex> parameters) { MyComplex p = parameters.get(0); if (p.type == ValueType.REAL) { return new MyComplex(Math.sqrt(p.real)); } return p.sqrt(); } }); addFunction(new Function("ARR", -1, "Create array") { @Override public MyComplex eval(List<MyComplex> parameters) { return new MyComplex(parameters); } }); addFunction(new Function("POLY", -1, "Treat array as Polynom") { @Override public MyComplex eval(List<MyComplex> parameters) { double[] d = MyComplex.getRealArray(parameters); PolynomialFunction p = new PolynomialFunction(d); return new MyComplex(p); } }); addFunction(new Function("DRVE", -1, "Make derivative of polynomial") { @Override public MyComplex eval(List<MyComplex> parameters) { PolynomialFunction p; if (parameters.get(0).isPoly()) { p = new PolynomialFunction(parameters.get(0).getRealArray()); } else { double[] d = MyComplex.getRealArray(parameters); p = new PolynomialFunction(d); } return new MyComplex(p.polynomialDerivative()); } }); addFunction(new Function("ADRVE", -1, "Make antiderivative of polynomial. Constant is always zero") { @Override public MyComplex eval(List<MyComplex> parameters) { PolynomialFunction p; if (parameters.get(0).isPoly()) { p = new PolynomialFunction(parameters.get(0).getRealArray()); } else { double[] d = MyComplex.getRealArray(parameters); p = new PolynomialFunction(d); } return new MyComplex(Misc.antiDerive(p)); } }); addFunction(new Function("PVAL", 2, "Compute value of polynom for the given argument.") { @Override public MyComplex eval(List<MyComplex> parameters) { if (parameters.get(0).isPoly()) { PolynomialFunction p = new PolynomialFunction(parameters.get(0).getRealArray()); double v = p.value(parameters.get(1).real); return new MyComplex(v); } throw new ExpressionException("first arg must be polynomial"); } }); addFunction(new Function("INTGR", 3, "Numerical integration") { @Override public MyComplex eval(List<MyComplex> parameters) { if (parameters.get(0).isPoly()) { PolynomialFunction p = new PolynomialFunction(parameters.get(0).getRealArray()); double start = parameters.get(1).real; double end = parameters.get(2).real; SimpsonIntegrator si = new SimpsonIntegrator(); double d = si.integrate(1000, p, start, end); return new MyComplex(d); } throw new ExpressionException("first arg must be polynomial"); } }); }