The VC calculator

Commands and operations

7 6 +

calculates 7+6=13.

+ can also be used to build strings. A string is a phrase inside quotes. The sum of a string and any item tacks on a string representation of the item to the original string. Thus

"x = " 3 +

produces the string "x = 3". Using this feature is good for explaining in output exactly what displayed data means.

- replaces the previous two items on the stack by their difference. Can subtract integers, real numbers, or vectors. Thus

7 6 -

calculates 7-6=1.

* replaces the previous two items on the stack by their product. Can multiply integers or real numbers. Also calculates the dot product of two vectors, or the scalar product of a vector and a scalar. Thus

7 6 *

calculates 7*6=42.

/ replaces the previous two items on the stack by their quotient. Can divide integers or real numbers. Thus

14 2 /

calculates 14/2 = 7.

fix requires a non-negative integer on the stack. It sets the number of decimal figures displayed in fixed point notation, and does not leave anything on the stack. Thus

5 fix 
4.0 =

displays 4.00000.

sci requires a non-negative integer on the stack. It sets the number of decimal figures displayed in scientific notation, and does not leave anything on the stack. Thus

3 sci
9 10 -6 ^ * =

def defines the previous item to be the item below it. The previous item must be a variable name such as @x or @longVariableName. A variable name is what you get by putting @ before the variable itself. Thus x is a variable and @x is its name. (We have to distinguish between the variable and its name because the results of putting them in a program are very different. When the calculator comes across the variable, it attempts to make a substitution. This is similar to the difference between a variable and a pointer to the variable in some programming languages.) Thus

5 @x0 def

defines the variable x0 to be 5. Subsequent occurrences of x0 (with some exceptions to be explained some other time) will be replaced by 5. You can assign values to vector coordinates this way, too. The command sequence 3 @v(2) def assigns the value of 3 to v(2) (but v has to be defined already).

cross replaces the previous two items by their cross product, if they are both three dimensional vectors.

floor replaces a number by the largest integer less than or equal to it. Thus 6.7 gets replaced by 6, while -6.7 gets replaced by -7.

sqrt replaces the previous item by its square root, if it is a non-negative number.

exp replaces the previous item x by e^x. Similarly for cos, acos, sin, log (which is the natural log).

atan2 has two arguments y and x in that order, and returns the angle coordinate of the point (x, y). (This odd and unfortunate choice of the order in which x and y are written conforms with that of most programming languages.)

^ is used for taking powers. Thus x y ^ returns x^y. This works only if x is positive or if y is an integer.

pi is a constant equal to 3.14159 ...

dup makes an extra copy of the item at the top of the stack.

pop just removes the item at the top of the stack. exch swaps the top two items on the stack.

lt, le, gt, ge, eq are tests on the previous two items, which should be numbers. The names stand for less than, less than or equals to, etc. The effect is to place either a true or a false on the stack.

ifelse uses the top three items on the stack, which should be true/false and two procedures. If true, it executes the first procedure, while if false it executes the second.

repeat can be used to perform loops. It requires an integer and a procedure immediately preceding it. A procedure is a sequence of instructions inside brackets { and }. Thus

1000 
10 { 1 - = } repeat

will output

999
998
997
996
995
994
993
992
991
990

break will break out of an enclosing loop. This should be used together with conditionals in order to halt a repeatloop. Thus the following program will print out only the numbers 10, 9, 8, 7, 6.

10 @x def
10 {
x 5 eq { break } { x = x 1 - @x def } ifelse
} repeat

stop will halt the calculator at the point it is inserted, at least in the window version being used here. You can then step through a few steps to see what is going on, and then run again. This is very useful for debugging.

Any error will be signalled by displaying an error message. You should never ignore one of these messages. It is possible that it is caused by a bug in the program, in which case you should make a bug report.

The calculator applet and this page were constructed by Bill Casselman.