CALC - An arbitrary precision calculator. by David I. Bell This is a calculator program with arbitrary precision arithmetic. All numbers are represented as fractions with arbitrarily large numerators and denominators which are always reduced to lowest terms. Real or exponential format numbers can be input and are converted to the equivalent fraction. Hex, binary, or octal numbers can be input by using numbers with leading '0x', '0b' or '0' characters. Complex numbers can be input using a trailing 'i', as in '2+3i'. Strings and characters are input by using single or double quotes. Commands are statements in a C-like language, where each input line is treated as the body of a procedure. Thus the command line can contain variable declarations, expressions, labels, conditional tests, and loops. Assignments to any variable name will automatically define that name as a global variable. The other important thing to know is that all non-assignment expressions which are evaluated are automatically printed. Thus, you can evaluate an expression's value by simply typing it in. Many useful built-in mathematical functions are available. Use the 'show builtins' command to list them. You can also define your own functions by using the 'define' keyword, followed by a function declaration very similar to C. Functions which only need to return a simple expression can be defined using an equals sign, as in the example 'define sc(a,b) = a^3 + b^3'. Variables in functions can be defined as either 'global' or 'local'. Global variables are common to all functions and the command line, whereas local variables are unique to each function level, and are destroyed when the function returns. Variables are not typed at definition time, but dynamically change as they are used. So you must supply the correct type of variable to those functions and operators which only work for a subset of types. By default, arguments to functions are passed by value (even matrices). For speed, you can put an ampersand before any variable argument in a function call, and that variable will be passed by reference instead. However, if the function changes its argument, the variable will change. Arguments to built-in functions and object manipulation functions are always called by reference. If a user-defined function takes more arguments than are passed, the undefined arguments have the null value. The 'param' function returns function arguments by argument number, and also returns the number of arguments passed. Thus functions can be written to handle an arbitrary number of arguments. The mat statement is used to create a matrix. It takes a variable name, followed by the bounds of the matrix in square brackets. The lower bounds are zero by default, but colons can be used to change them. For example 'mat foo[3, 1:10]' defines a two dimensional matrix, with the first index ranging from 0 to 3, and the second index ranging from 1 to 10. The bounds of a matrix can be an expression calculated at runtime. Lists of values are created using the 'list' function, and values can be inserted or removed from either the front or the end of the list. List elements can be indexed directly using double square brackets. The obj statement is used to create an object. Objects are user-defined values for which user-defined routines are implicitly called to perform simple actions such as add, multiply, compare, and print. Objects types are defined as in the example 'obj complex {real, imag}', where 'complex' is the name of the object type, and 'real' and 'imag' are element names used to define the value of the object (very much like structures). Variables of an object type are created as in the example 'obj complex x,y', where 'x' and 'y' are variables. The elements of an object are referenced using a dot, as in the example 'x.real'. All user-defined routines have names composed of the object type and the action to perform separated by an underscore, as in the example 'complex_add'. The command 'show objfuncs' lists all the definable routines. Object routines which accept two arguments should be prepared to handle cases in which either one of the arguments is not of the expected object type. These are the differences between the normal C operators and the ones defined by the calculator. The '/' operator divides fractions, so that '7 / 2' evaluates to 7/2. The '//' operator is an integer divide, so that '7 // 2' evaluates to 3. The '^' operator is a integral power function, so that 3^4 evaluates to 81. Matrices of any dimension can be treated as a zero based linear array using double square brackets, as in 'foo[[3]]'. Matrices can be indexed by using commas between the indices, as in foo[3,4]. Object and list elements can be referenced by using double square brackets. The print statement is used to print values of expressions. Separating values by a comma puts one space between the output values, whereas separating values by a colon concatenates the output values. A trailing colon suppresses printing of the end of line. An example of printing is 'print \"The square of\", x, \"is\", x^2\'. The 'config' function is used to modify certain parameters that affect calculations or the display of values. For example, the output display mode can be set using 'config(\"mode\", type)', where 'type' is one of 'frac', 'int', 'real', 'exp', 'hex', 'oct', or 'bin'. The default output mode is real. For the integer, real, or exponential formats, a leading '~' indicates that the number was truncated to the number of decimal places specified by the default precision. If the '~' does not appear, then the displayed number is the exact value. The number of decimal places printed is set by using 'config(\"display\", n)'. The default precision for real-valued functions can be set by using 'epsilon(x)', where x is the required precision (such as 1e-50). There is a command stack feature so that you can easily re-execute previous commands and expressions from the terminal. You can also edit the current command before it is completed. Both of these features use emacs-like commands. Files can be read in by using the 'read filename' command. These can contain both functions to be defined, and expressions to be calculated. Global variables which are numbers can be saved to a file by using the 'write filename' command.