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Setup for README.md and improved calc overview
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README.md
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# What is calc?
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Calc is an interactive calculator which provides for easy large
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Otherwise, it enters interactive mode. In this mode, it accepts
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commands one at a time, processes them, and displays the answers.
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In the simplest case, commands are simply expressions which are
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evaluated. For example, the following line can be input:
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```sh
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3 * (4 + 1)
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```
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and the calculator will print:
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```sh
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15
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```
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Calc as the usual collection of arithmetic operators +, -, /, * as
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well as ^ (exponentiation), % (modulus) and // (integer divide).
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For example:
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```sh
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3 * 19^43 - 1
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```
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will produce:
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```sh
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29075426613099201338473141505176993450849249622191102976
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```
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Notice that calc values can be very large. For example:
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```sh
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2^23209-1
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```
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will print:
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```sh
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402874115778988778181873329071 ... many digits ... 3779264511
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```
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The special '.' symbol (called dot), represents the result of the
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last command expression, if any. This is of great use when a series
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of partial results are calculated, or when the output mode is changed
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and the last result needs to be redisplayed. For example, the above
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result can be modified by typing:
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```sh
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. % (2^127-1)
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```
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and the calculator will print:
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```sh
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47385033654019111249345128555354223304
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```
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For more complex calculations, variables can be used to save the
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intermediate results. For example, the result of adding 7 to the
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previous result can be saved by typing:
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```sh
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curds = 15
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whey = 7 + 2*curds
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```
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Functions can be used in expressions. There are a great number of
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pre-defined functions. For example, the following will calculate
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the factorial of the value of 'whey':
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```sh
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fact(whey)
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```
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and the calculator prints:
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```sh
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13763753091226345046315979581580902400000000
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```
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The calculator also knows about complex numbers, so that typing:
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```sh
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(2+3i) * (4-3i)
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cos(.)
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```
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will print:
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```sh
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17+6i
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-55.50474777265624667147+193.9265235748927986537i
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```
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The calculator can calculate transcendental functions, and accept and
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display numbers in real or exponential format. For example, typing:
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```sh
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config("display", 70)
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epsilon(1e-70)
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sin(1)
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```
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prints:
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```sh
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0.8414709848078965066525023216302989996225630607983710656727517099919104
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```
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Calc can output values in terms of fractions, octal or hexadecimal.
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For example:
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```sh
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config("mode", "fraction"),
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(17/19)^23
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base(16),
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(19/17)^29
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```
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will print:
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```sh
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19967568900859523802559065713/257829627945307727248226067259
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0x9201e65bdbb801eaf403f657efcf863/0x5cd2e2a01291ffd73bee6aa7dcf7d1
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```
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All numbers are represented as fractions with arbitrarily large
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numerators and denominators which are always reduced to lowest terms.
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Real or exponential format numbers can be input and are converted
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to the equivalent fraction. Hex, binary, or octal numbers can be
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input by using numbers with leading '0x', '0b' or '0' characters.
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Complex numbers can be input using a trailing 'i', as in '2+3i'.
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Strings and characters are input by using single or double quotes.
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Commands are statements in a C-like language, where each input
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line is treated as the body of a procedure. Thus the command
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line can contain variable declarations, expressions, labels,
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conditional tests, and loops. Assignments to any variable name
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will automatically define that name as a global variable. The
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other important thing to know is that all non-assignment expressions
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which are evaluated are automatically printed. Thus, you can evaluate
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an expression's value by simply typing it in.
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Many useful built-in mathematical functions are available. Use the:
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```sh
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help builtin
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```
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command to list them.
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You can also define your own functions by using the 'define' keyword,
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followed by a function declaration very similar to C.
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```sh
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define f2(n)
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{
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local ans;
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ans = 1;
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while (n > 1)
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ans *= (n -= 2);
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return ans;
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}
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```
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Thus the input:
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```sh
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f2(79)
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```
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will produce;
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```sh
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1009847364737869270905302433221592504062302663202724609375
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```
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Functions which only need to return a simple expression can be defined
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using an equals sign, as in the example:
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```sh
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define sc(a,b) = a^3 + b^3
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```
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Thus the input:
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```sh
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sc(31, 61)
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```
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will produce;
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```sh
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256772
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```
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Variables in functions can be defined as either 'global', 'local',
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or 'static'. Global variables are common to all functions and the
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command line, whereas local variables are unique to each function
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level, and are destroyed when the function returns. Static variables
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are scoped within single input files, or within functions, and are
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never destroyed. Variables are not typed at definition time, but
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dynamically change as they are used.
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For more information about the calc language and features, try:
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```sh
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help overview
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```
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Calc has a help command that will produce information about
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every builtin function, command as well as a number of other
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aspects of calc usage. Try the command:
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```sh
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help help
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```
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for and overview of the help system. The command:
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```sh
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help builtin
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```
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provides information on built-in mathematical functions, whereas:
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```sh
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help asinh
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```
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will provides information a specific function. The following
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help files:
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```sh
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help command
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help define
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help operator
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help statement
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help variable
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```
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provide a good overview of the calc language. If you are familiar
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with C, you should also try:
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```sh
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help unexpected
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```
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It contains information about differences between C and calc
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that may surprize C programmers.
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