00001 #include "MusimatTutorial.h" 00002 MusimatTutorialSection(B0115) { 00003 Print("*** B.1.15 Functions ***"); 00004 /***************************************************************************** 00005 00006 B.1.15 Functions 00007 00008 Functional notation in mathematics allows us to encapsulate and name arithmetic expressions. For 00009 example, if we have defined the function f (a, b) = a + b, then f stands for a + b. The value or values 00010 in parentheses after a function name, called arguments, supply the function with inputs. Functions 00011 also typically return a result. For example, using this definition of f, 7 = f (3, 4). 00012 00013 Programming languages typically come with a set of predefined functions for the most common 00014 necessities, and they also allow new functions to be created. For example, in Musimat all oper- 00015 ators also have a functional representation, so writing 00016 *****************************************************************************/ 00017 00018 Real x = Divide(11.0, 4.0); 00019 Print("x=", x); 00020 00021 /***************************************************************************** 00022 is the same as writing 00023 *****************************************************************************/ 00024 00025 Real e = 11.0/4.0; 00026 Print("e=", e); 00027 00028 /***************************************************************************** 00029 In this case, e is set to the quotient, 2.75. Real division is performed because both numerator 00030 and denominator are reals. If we want to perform integer division, both numerator and denominator 00031 must be integers. We could write 00032 *****************************************************************************/ 00033 00034 Integer f = Divide(11, 4); 00035 Print("f=", f); 00036 00037 /***************************************************************************** 00038 or equivalently, 00039 *****************************************************************************/ 00040 00041 Integer g = 11/4; 00042 Print("g=", g); 00043 00044 /***************************************************************************** 00045 In either case, f and g are set to the quotient, 2, and the remainder is discarded. To get the remainder after 00046 integer division we can write 00047 *****************************************************************************/ 00048 00049 Integer h = Mod( 11, 4 ); // remainder of integer division 00050 Print("h=", h); 00051 00052 /***************************************************************************** 00053 The variable h is set to 3, the remainder of 11/4. For positive integers m and n, Mod(m, n) 00054 lies between 0 and n - 1. Why is this function called Mod instead of, say, Remainder? See appen- 00055 dix A, A.6. The equivalent operator form for remaindering also looks a little strange: 00056 *****************************************************************************/ 00057 00058 Integer i = 11 % 4; 00059 Print("i=", i); 00060 00061 /***************************************************************************** 00062 The % sign does not have its usual meaning of "percent" in Musimat. Instead, it means "remain- 00063 der of integer division." Mod and % can only be applied to integer operands. 00064 00065 Some useful built-in functions are not associated with operators. Exponentiation is performed 00066 by the function Pow(). These three statements, 00067 *****************************************************************************/ 00068 00069 Real base = 10.0; 00070 Real exp = 2.0; 00071 Real j = Pow(base, exp); 00072 Print("j=", j); 00073 00074 /***************************************************************************** 00075 are equivalent to writing "j = 10.0 to the power of 2.0", and the result stored in j is 100.0. 00076 Going the other way: Log10(x) is equivalent to "log base 10 of x", and 00077 *****************************************************************************/ 00078 00079 Real k = Log10(100.0); 00080 Print("k=", k); 00081 00082 /***************************************************************************** 00083 sets k to 2. 00084 00085 Another built-in function, Print(), allows us to observe the value of a variable or expression. 00086 When executed, the statements 00087 *****************************************************************************/ 00088 00089 Real l = 11.0/4.0; 00090 Print("l=", l); 00091 00092 /***************************************************************************** 00093 display the value of l, or 2.75. The way in which the value is displayed varies with the type of the 00094 expression and the type of computer. If the computer is a person, for example, he or she might say "two 00095 point seven five." If it is an electromechanical computer, it might show the value on a display screen. 00096 00097 When the predefined function Halt() is executed, the method in progress stops at that step in 00098 the program. The argument to Halt(), if any, can be used to indicate the answer or result obtained 00099 by the program up to that point. 00100 00101 One final built-in function is Random(), which returns a real number in the range of 0.0 to 1.0 00102 chosen at random. 00103 *****************************************************************************/ 00104 } 00105 00107 /* $Revision: 1.2 $ $Date: 2006/09/05 06:32:25 $ $Author: dgl $ $Name: $ $Id: B0115.cpp,v 1.2 2006/09/05 06:32:25 dgl Exp $ */ 00108 // The Musimat Tutorial © 2006 Gareth Loy 00109 // Derived from Chapter 9 and Appendix B of "Musimathics Vol. 1" © 2006 Gareth Loy 00110 // and published exclusively by The MIT Press. 00111 // This program is released WITHOUT ANY WARRANTY; without even the implied 00112 // warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 00113 // For information on usage and redistribution, and for a DISCLAIMER OF ALL 00114 // WARRANTIES, see the file, "LICENSE.txt," in this distribution. 00115 // "Musimathics" is available here: http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=10916 00116 // Gareth Loy's Musimathics website: http://www.musimathics.com/ 00117 // The Musimat website: http://www.musimat.com/ 00118 // This program is released under the terms of the GNU General Public License 00119 // available here: http://www.gnu.org/licenses/gpl.txt 00120
1.7.2