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On Line RPN Calculator


Contents
Intro
Screen Display Control
Basic Math
Transendental Functions
Loan and Payment Functions
Statistical Functions
Unit Conversions
Stack Control
Variables
User Defined Functions
RPN Calculator Examples


Intro

The RPN calculator is a powerful tool for doing things you might normally do with a calculator, and more. It uses Reverse Polish Nomenclature (RPN) in its expressions, numbers first, followed by operators, similar in concept to my trusty HP HP48GX RPN Expandable Graphic Calculator. For example, to add two numbers: 25 19 + places the two numbers on the stack, and performs the add operation, leaving the result on the stack.

The RPN calculator gives users the ability to create their own functions, and with a single function they could make calculations that fill all 26 variables. This minimal programming ability is what amplifies the calculator's usability above most all traditional calculators. It's handily available for anyone with an internet connection, ready for any college or university student, or anyone else needing math, financial, statistical or other general calculater functions.

All operators work with the stack. Math operators work with the top value(s) on the stack and leave results on the stack. Memory operators move values either from the stack to the variables a thru z, or from the variables to the stack.

The program is different from most calculators in that one can either enter commands into the command window, or click on function buttons. It's also different in that with a typical calculator, clicking on a button performs the indicated operation. With this calculator, clicking on a button other than Enter places the command in the command window. Multiple calculations can be entered, then pressing the keyboard enter key or clicking on the Enter button executes the command(s).

Because some of the more powerful aspects are best implemented with a keyboard, the calculator works very well with Desktops, Laptops, and Chromebooks. However, the keypad utilty does make it work pretty well with Tablets as well. The RPN calculator has been successfully tested with Google Chrome, Firefox, Seamonkey, Opera, and an Android tablet and Android phone.

The command box concept may seem awkward at first, but offers some real power as you learn the calculator. For example, one can enter the command: 10 20 30 40 50 60 all nput a to put the values 10 thru 60 into variables a thru f, all as one statement. Commands are saved in a history and can be recalled for editing and re-use by clicking on the History button. More power is available when you learn how to define your own operations


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Display Control Operators

Screen control operators select the keypad mode to display, and the numeric display format The keypad selections are only available through button clicks. The numeric display functions can be keyboard or keypad selected.

ExampleResult
eeSwitch numeric display to/from exponential format
3 ndSwitch numeric display to 3 decimal places
clsClear all values from stack
clm Clear all variables
Math Ops Sets keypad to basic math operators
Stats Ops Sets keypad to statistical operators
Units Ops Sets keypad to unit conversion operators
User Keys Sets keypad to user defined operators
User Defs Sets keypad to user definition display

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Basic Commands

The basic math operators, like +, -, *, / (for add, subtract, multiply, and divide), all work with pairs of numbers on the stack.

ExampleResult
30 neg Negate 30, leaves -30
30 +/- Keypad negate 30, leaves -30
10 20 + Puts 10 and 20 on the stack and adds them, leaving the sum.
30 14 - Subtracts 14 from 30 (top is subtracted from next level).
3 8 * Multiplies 3 times 8, leaving result on stack.
33 12 / Divides 33 by 12, leaving result on stack.
10 sqr Square the number 10
13 sqrt Compute square root of 13
2 1/x Compute reciprocal of 2, result is 0.5
int Leave integer portion of top stack value
frac Leave fractional portion of top stack value
min Leave mininum of top two stack on stack
max Leave maximum of top two stack on stack

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Transcendental Operators

Note, all of the trig functions work with radians. Use the rad operator to turn the top stack value into radians, and deg operator to go back to degrees. For example, to get sine of 30 degrees: 30 rad sin. To get arc-sine of .5 as degrees: .5 asin deg.

ExampleResult
pi Put value of PI on the stack
30 rad sin Returns sine of 30 degrees (converts to radians first)
25 rad cos Returns cosine of 25 degrees.
45 rad tan Returns tangent of 45 degrees.
.5 asin deg Returns arc-sine of .5 as degrees.
.5 acos deg Returns arc-cosine of .5 as degrees.
.5 atan Returns arc-tangent of .5 as radians.
300 log Returns the base 10 log of 300.
300 ln Returns the base e log of 300.
3 exp10 Raises 10 to the power of 3.
3 exp Raises e to the power of 3.
12 3 ^ Raises 12 to the 3rd power.

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Loan, Payment, and Date Functions

The calculator can calculate loan values for given payment, interest, and number of period values, or calculate payment values for given loan, interest, and number of period values. Each operation expects the values on the stack in a specific order: loan interest n-periods or payment interest n-periods. Interest is percent per year, and periods are months.

ExampleResult
5000 6 36 pmtCalculates payment for a $5000 loan at 6 percent for 36 months
200 6 36 loanCalculates loan value for a $200 payment at 6 percent for 36 months
200 6 36 12 ppaidCalculates principal paid on $200 loan, 6 pct, 36 months, after month 12
200 6 36 12 pleftCalculates principal left on $200 loan, 6 pct, 36 months, after month 12
datePlaces month, day, and year on stack

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Statistical Functions

The RPN calculator has a number of statistical and probability functions. These often work on several values at once, either on the stack or in a consecutive range of variables. For example, the fit function will compute the slope and offset of a range of values assuming that the X values of a Y=mX+b equation is a simple count, 1, 2, 3, ... . This will work for any data that's obtained at equal increments in time for example, like daily, or monthly.

The res function, given the same range used in the fit function, will compare the range variable values against the computed line and leave a corresponding list of fit errors on the stack. For example: fit a g computes a slope and offset from values in a thru z, and res a g will compare the computed line values with the values in a thru g, leaving the errors on the stack. The computed slope and offset are left on the stack, and saved internally for options that need them.

The x2y function uses the most recent fit results to compute corresponding Y values for any given range of X values on the stack, again assuming Xs of the fit interval were 1 thru number_of_points. This can be used to compute Y values for any X values, within or outside of the original fit range. For example, for fit a e, variables a thru e amount to 5 points, which assume X values from 1 to 5. To extrapolate the next few Y values from the fit, put the desired X values on the stack and use the x2y operator. 6 13 x2y will extrapolate the 5 point line to give Y values for X values 6 thru 13.

X

The do operator iterates an operation, placing each value of a variable range on the stack prior to calling the desired function. The operator looped upon must be a single operator, but using a user defined operation, this can lead to significant power.

As a simple example, do a f log computes the log of each value from variables a thru f, leaving the results on the stack. 5 nput n would place the log values in the display's second column beside the original values in the expected order.

But suppose you wanted the log of each number in base 2? Since do can only repeatedly execute a single operation, just define your own operator as follows: def log2   log   2 log /, which takes the log of a passed in (on the stack) value, and divides by the log of two, which leaves the log in base 2. Then do a f log2 would execute your definition, which has been reduced to a single name using def.

ExampleResult
6 !Computes 6 factorial, or 720
13 3 nCrComputes the number of combinations of 3 in 13
13 3 nPrComputes the number of permutations of 3 in 13
0 12 2 seqGenerates sequence from 0 to 12 with increment 2
sum a fComputes the sum of variables a thru f
avg a fComputes the average of variables a thru f
var a fComputes the variance of variables a thru f
std a fComputes the std deviation of variables a thru f
ssumComputes the sum of all stack values
savgComputes the average of all stack values
svarComputes the variance of all stack values
sstdcomputes the std deviation of all stack values
fit a fFits a line thru variables a to f and leaves offset and slope on stack
res a fComputes the residuals of the last line fit
7 10 x2yExtrapolates the line fit at X values 7 to 10
do a c sqrtComputes sqrt of values in a thru c,
leaving 3 values on stack

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Unit Conversion Operators

The calculator has a number of built in unit conversions. These can be used in sequence to get conversions not already defined. For example, to get a conversion from kilometers to inches: 3 km2mi mi2yd yd2ft ft2in. Of course, if you needed such a conversion often, you could define it as a new operation thus: def km2in   km2mi mi2yd yd2ft ft2in. Then you could use the new operation as follows: 10 km2in.

ExampleResult
30.5 d2hms converts degrees to hms format: 303000
304500 hms2d converts hms format to degrees: 30.75
3 ft2in Converts 3 feet to 36 inches
42 in2ft Converts 42 inches to 3.5 feet
4 yd2ft Converts 4 yards to 12 feet
30 ft2yd Converts 30 ft to 10 yards
2640 yd2mi Converts 2640 yards to 1.5 miles
1.5 mi2yd Converts 1.5 miles to 2640 yards
3 in2cm Converts 3 inches to 7.62 cm
7.62 cm2in Converts 7.62 cm to 3 inches
6 ft2m Converts 6 feet to 1.8288 meters
1.8288 m2ft Converts 1.8288 meters to 6 feet
3 yd2m Converts 3 yards to 2.7432 meters
2.7432 m2yd Converts 2.7432 meters to 3 yards
3 mi2km Converts 3 miles to 4.82... km
10 km2mi Converts 10 km to 6.2... miles
300 ci2cc Converts 300 cubic inches to 4916... cc
5200 cc2ci Converts 5200 cc to 317... cubic inches
6 qt2lt Converts 6 quarts to 5.6... liters
10 lt2qt Converts 10 liters to 10.5... quarts
10 gal2lt Converts 10 gallons to 37.8... liters
10 lt2gal Converts 10 liters to 2.6... gallons
6 gal2cf Converts 6 gallons to 0.8... cubic feet
3 cf2gal Converts 3 cubic feet to 22.4... gallons
30 lb2kg Converts 30 pounds to 13.6... kilograms
30 kg2lb Converts 30 kilograms to 66.1... pounds
95 f2c Converts 95 deg Fahrenheit to 35 deg Celsius
40 c2f Converts 40 deg Celsius to 104 deg Fahrenheit

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Stack Control

Don't be confused by the stack. It's easy to view it as an array, but it's actually just a history and temporary repository for values used by operations. The newest entry is on top, and the older ones below. Operators that work on stack numbers use the newest ones (top values).

If you enter 10, 20, and 30, for example, the stack shows:

30
20
10

The 10 was entered first, and is thus on the bottom of the stack. However, if you use 3 nput a to put the 3 numbers into a, b, and c, you'll see:

a 10
b 20
c 30

The oldest entry is in a, and so on. Why? Because you'll often want to preset variables for computations, and the natural inclination is to put the values in consecutive variable order, like a series of interest values in a thru e. For example: 2 4 5 8 10 all nput a would show a with 2, b with 4, and so on. It seems right. So the variables can be thought of as an array, but remember that the stack is just a history. That can make it appear upside down for the bulk memory operations.

It's often handy to be able to manipulate values on the stack, especially when making user definitions. Most of these move values from the stack to variables, or vice versa. Some manipulate the top few values, and are simple but often indispensable operators.

ExampleResult
dup Duplicate the top value on the stack
swap Swap the top two values on the stack
drop Drop the top value from the stack
cls Clear all stack values
> zStore top stack value into z
aPlace value in variable a on top of stack
put x zPut top 3 stack values into z, y, and x
3 nput a Put top 3 stack values into c, b, and a
get a dCopy variabls a thru d onto stack (a oldest)
3 nget aCopy 3 variables starting with a onto stack

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How To Use Variables

The calculator has 26 variables, labeled a thru z. You can store the top value to a variable or place the contents of a variable on the stack. You can also store a number of stack values (or all) to a contiguous range of variables with a single command, and likewise place a range of variable values back onto the stack.

ExampleResult
allPut stack depth on top of stack
> xStore top stack to variable x
= xStore top stack to variable x
a Put value in variable a onto stack
put a c Put top 3 stack values into a thru c
4 nput w Put 4 stack values in w thru z
all nput a Put all stack values starting at a
get c e Get values in c thru e and put onto stack
3 nget x Get 3 values starting at x and put onto stack

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User Defined Functions

One of the most powerful features of the calculator is the ability of a user to create his/her own function definitions. Each definition can use any constants, variable references, and existing functions. User definitions can also refer to other user definitions.

The User Keys button on the keypads brings up a keypad that lists user defined functions as click-able functions. The User Defs keypad shows the actual definitions of each user defined function. Note that any functions that used the do operator have been expanded with the do replaced with the respective variable references and repeated function reference.

A simple example might be to define a word to aid in the calculation of payment values for long term loans, where months is cumbersome. You could do: def years 12 * as a new function, which multiplies a year value on the stack by 12, converting it into months. Using it with the pmt function would be: 75000 6 30 years pmt. You see that prior to the execution of the pmt operator, loan value, interest, and months would be on the stack.

If you've allowed cookies, the save command will save the calculator state (variables, numeric display format, and user defs) in year long cookies. If you want to get rid of all browser cookies, you can load the RPN calculator web page first, clear cookies, then save, to allow clearing of all other cookies, but still keeping your user defs.

The ed function, such as: ed years to edit definition years, will put the definition of an operation in the command window. After editing, the keyboard enter or Enter button will re-save the new definition. clearing the command window before Enter will simply remove the definition.

As new and more useful definitions of your own occur to you, you may find that you wish you could re-arrange your user-defined buttons. With the move command, you can do that. The move function is available on the User Keys and User Defs keypads. To use it, just click on move, then the user definition you'd like to move, then the user definition that you wish to have preceding the moved definition. move places the first definition after the second one.

It's possible to have 75 or more user defs in a cookie. The User Keys keypad displays up to 25 at a time. The Next and Prev buttons allow you to move through your user defs if you have more than 25 defined. If you are at the first row, the Prev button doesn't show. Likewise, if your are at the end of your defs, the Next button doesn't show.

For example, assume you have a sum1 command, and some time later you create a sum2 command. But they are just in the user definition list in the order you created them, and may not be together. So you could in order clickmove sum2 sum1 to have button sum2 placed just after sum1. Use the move function to arrange your user buttons in the most comfortable order.

ExampleResult
def years 12 *Defines an op that would convert years to months
def mypmt   5000 swap 36 pmtDefines an op that would assume a 5000 loan for 36 months,
but take interest from the stack. Like 12 mypmt.
See how swap puts arguments in proper order?
undefRemoves most recent def, but puts the def command in history
sdefsList defs to screen so user can copy and save them locally. Pasting the saved text in command window and Enter will restore them.
cldefsRemove all user definitions, but place in history
ed yearsPlaces definition of user def years in command window for editing
move user1 user2Moves the user command user1 just after user command user2
NextIf shown, moves forward one row of user defs
PrevIf shown, moves back one row of user defs
saveSave current calculator state in year long cookies.
Saves variables, numeric display mode, and user definitions

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