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RPN --- A simulation of a Hewlett-Packard scientific calculator. ______________________________ SYNOPSIS rpn -b <-t top> <-l left> <-c [config-file]>> All command-line arguments are optional. Angle brackets indicate associated arguments, square braces indicate optional filenames. ______________________________ Contents: SYNOPSIS Contents DESCRIPTION A Quick Sketch of the HP Calculator Style. AVAILABLE FUNCTIONS FUNCTIONS CONSTANTS UNIT CONVERSION functions TIME functions ANGULAR functions MEMORY functions STATISTICAL functions PRINTING MISCELLANEOUS SCREEN COLORS MEANS STANDARD DEVIATION LINEAR REGRESSION CONFIGURATION FILE KNOWN BUGS ACKNOWLEDGEMENTS VERSION HISTORY AUTHOR ______________________________ DESCRIPTION RPN is another calculator, this one using rpn logic in the manner of my dear departed HP-29c (R.I.P.). Almost all of the functions are implemented. There is no programmability feature. All math is done in double-precision floating-point. There are 100 memory "registers" (rather than the HP-29c's 31 "registers"), referred to as M[0] .. M[99]. The memory registers are long-double-precision, to give the statistical functions somewhat more accuracy. A display is drawn on the right side of the screen, showing the stack registers, LastX register, last-executed-function, the function name currently being entered, and the number base in use. Two Help screens can be called up via the F1 function key; these list the available functions and the hexadecimal "digits". The program was written and tested on a CGA display; it has been reported to work on a Hercules display. (version 2.1) Optional arguments -t and -l can be supplied to open the display at a specified upper-left corner. Once opened, the display may be repositioned as desired by toggling on the ScrollLock key and then using the cursor keys. The Help screens may overlap the display in this case, and will get turned off as the display moves. ScrollLock status is displayed in the trig-mode window, if it's on. (version 3.0) Optional argument -b allows use of the slower BIOS output mode, which may be work on less-compatible machines. Optional argument -c allows use of a configuration file. If a filename is supplied, that file is used (if it exists). Without a filename, RPN will look for an environment variable named RPN, whose value is taken as the fully path-qualified name of the configuration file. If the environment variable is absent, RPN will look for the filename CONFIG.RPN in the current directory and in the root directory. If no configuration file is found, the -c option is a harmless error. With version 3.0, RPN departs from straight interpretation of an HP-29, by adding a number of numerical and controlling functions. ______________________________ A Quick Sketch of the HP Calculator Style. "RPN" is Reverse Polish (in honor of Lukasiewiez) Notation. Numbers are entered onto a 4-deep stack, then a function is invoked. The function removes whatever arguments it needs from the stack, and puts its result on the stack instead. The previous top-of-stack is saved in the "LastX" register, from which it can be recalled for reuse or undoing of the last function. The four stack "registers" are named, from top to bottom, X, Y, Z, and T. When a function pops the stack the T register replicates itself. ______________________________ AVAILABLE FUNCTIONS Some functions are represented by single keys. Most of them are represented by a multiple-character, carriage-return- terminated string. This string is processed character by character (necessary with console input). Some functions have more than one "name" for user convenience. In the following list, a comma separates alternate forms for a function. A `#' indicates an integer representing a memory register (0..99), a precision (number of displayed places, 1..19), or a number base (8,10,16 work). <CR>, <SPACE>, and <ESC> are keys. A `^' indicates a control character; a `@' indicates an ALTernate character. All other characters must be entered as shown. FUNCTIONS + Y + X - Y - X * Y * X / Y / X % X percent of Y (Y unchanged) I invert X register to (1.0 / X) pow, ^ power function (Y^X or Y raised-to-power X) pow10, p10 anti-common-log (10^X) exp anti-natural-log (e^X or exp(X)) ln natural logarithm of X lg base-2 logarithm of X log base-10 (common) logarithm of X !, fact factorial of X register ( == gamma(X+1) ) gamma gamma function of X register ( == (X-1)! ); gamma values are approximated to five decimal places (by table lookup) sqr square of X sqrt square root of X abs absolute value of X int integer portion of X frac fractional portion of X L retrieve last X value back into X register C clear X register X exchange X register and Y register N, ' change-sign (negate) X register (quote-mark is alternate 1-key form, for convenience) This key changes the sign of the mantissa or of the exponent, if either is being entered. ru, UpArrow roll stack up rd, DownArrow roll stack down clrstk clear all four stack registers sinh hyperbolic sine of X cosh hyperbolic cosine of X tanh hyperbolic tangent of X isinh inverse hyperbolic sine of X icosh inverse hyperbolic cosine of X itanh inverse hyperbolic tangent of X csch hyperbolic cosecant of X sech hyperbolic secant of X coth hyperbolic cotangent of X icsch inverse hyperbolic cosecant of X isech inverse hyperbolic secant of X icoth inverse hyperbolic cotangent of X CONSTANTS pi load value of pi (3.14159...) into X register c load 299792.4562 (km/second; speed of light in free space) fc load 1797610211686.842 (c, in furlongs/fortnight) planck load 6.6261965e-34 (Joules/second; Planck's Constant) avogadro load 6.0221694e23 (/ mole; molecules / mole) epsi load 8.854e-12 (Farads/meter; permittivity of free space (epsilon0)) UNIT CONVERSION functions -- all these alter the X-register acres convert hectares to acres cal convert Joules to calories (not Kilocal.) celsius convert Fahrenheit to Celsius cuinch convert gallons to cubic inches deg convert X from degrees to radians fahr convert Celsius to Fahrenheit feet convert meters to feet furlongs convert yards to furlongs gal convert liters to gallons hectares convert acres to hectares igal convert cubic inches to gallons joules convert calories to Joules kg convert pounds (avoirdupois) to kilograms km convert miles to kilometers lb convert kilograms to pounds (avdp.) liters convert gallons (U.S. liq.) to liters ly convert meters to lightyears lymeters convert lightyears to meters meters convert feet to meters miles convert kilometers to miles mph convert miles/hour to meters/second mps convert meters/second to miles/hour rad convert X from radians to degrees yards convert furlongs to yards TIME functions -- convert between decimal-formatted hours and "sexagesimal-formatted" hours, where sexagesimal, or base 60, is represented as HH.MMSSfff... Here HH represents hours, MM represents minutes, SS represents seconds, and fff... represents fractions of seconds. (HH may be more than two digits.) Base conversion and roundoff anomalies occasionally produce a value such as "12.1860" instead of "12.1900". Values are rounded to nanoseconds to alleviate this. Usage note: these functions also convert degrees-minutes-seconds to and from decimal degrees. hms convert decimal hours in X register to sexagesimal format hrs convert sexagesimal formatted hours in X register to decimal format. ANGULAR functions ^D put calculator in "Degree" mode (default) ^R put calculator in "Radians" mode rad convert X from degrees to radians deg convert X from radians to degrees sin sine of X cos cosine of X tan tangent of X asin, arcsin arcsine of X acos, arccos arccosine of X atan, arctan arctangent of X atan2 arctangent of the ratio Y-register / X-register (better accuracy for some values) polar convert X,Y Cartesian coordinates (in X-register and Y-register) To R,Theta polar coordinates (R -> X, Theta in radians -> Y) rect convert polar coordinates (R in X, Theta in Y) into X,Y Cartesian coordinates MEMORY functions (see also STATISTICAL) -- in the following the `#' symbol refers to an address in the range 0..99, or `i' (meaning use M[0] contents as an address). `#' is a "metanumber", always specified in base 10. clrmem load 0.0 into all Memory locations clrblk load 0.0 into range of Memory locations, with the lowest index in Y reg. and highest index in X reg. sto#, S# store X into M[ # ] sto+#, S+# add X-contents to M[ # ] sto-#, S-# subtract X-contents from M[ # ] sto*#, S*# multiply M[ # ] by X-contents sto*#, S/# divide M[ # ] by X-contents rcl#, R# recall M[ # ] into X-register STATISTICAL functions rcls, Rs recall M[11] into X, M[13] into Y clrsum load 0.0 into each of M[10] .. M[17], load 1.0 into M[18] and M[19]. sum+, ] add X into M[11], X*X into M[12], Y into M[13], Y*Y into M[14], X*Y into M[15]; add inverse of X into M[16], inverse of Y into M[17]; multiply X into M[18], multiply Y into M[19]; increment M[10] (X saved in lastX-reg., M[10] into X-reg.) sum-, [ subtract X from M[11], X*X from M[12], Y from M[13], Y*Y from M[14], X*Y from M[15]; subtract inverse of X from M[16], inverse of Y from M[17]; divide M[18] by X, divide M[19] by Y; decrement M[10] (used to undo a mistaken sum+ function) mean M[11] / M[10] into X, M[13] / M[10] into Y sd sample std.dev. of X's and Y's into X-register and Y-register respectively (see "STANDARD DEVIATION" below) geomean n'th root of M[18] into X, n'th root of M[19] into Y (M[10] == n) harmean M[10] / M[16] into X, M[10] / M[17] into Y clrlin load 0.0 into each of M[90] .. M[99] linreg perform a linear regression on X-Y pairs accumulated in the summation registers. B1 coefficient into X, B0 coeff. into Y, s(y|x) into Z, r-squared into T, covariance into LastX. * Memory registers also affected; see below. linstats retrieve statistics from a previous linear regression. s(B1) into X, t(B1) into Y, s(B0) into Z, t(B0) into T, F-ratio into LastX. * See below. interpy perform linear interpolation on x value in X, put resulting y value back into X. This uses B0 and B1 coefficients in registers 90 and 91, and is compatible with the `linreg' function. Also see `lincoeffs'. interpx perform inverse linear interpolation on x value in X, put resulting y value back into X. This uses B0 and B1 coefficients in registers 90 and 91, and is compatible with `linreg'. See `lincoeffs'. lincoeffs calculate and store B0 and B1 coefficients into Memory[90] and Memory[91], using two points: x1 from T, y1 from Z, and x2 from Y, y2 from X. Order of x and y input values differs from `linreg'. PRINTING <F2> Toggle saving of results. If a savefile is already open it is closed. Otherwise a file is opened in the current directory. If a name has been typed in, like a function (but not entered), then that is the filename. Otherwise the name "save-out.rpn" is used. As each function is performed, its name and the contents of the Y, X, and LastX registers are written. prtstk print the T, Z, Y, X, and LastX registers prtreg print the contents of all non-zero memories prtsum print the contents of the summation memories M[10]..M[19]; also the means, stddev's, geometric means, and harmonic means prtlin print the results of a linear regression. These are precisely the outputs of the `linreg' and `linstats' functions. MISCELLANEOUS -- keys used in entering numbers and controlling the calculator. In the following, '#' is a "metanumber", specified in base 10. E# exponent of number currently being entered (mantissa is set to 1 if no current value) P# display # decimal places of the X register (# range should be 0..15) B# display numbers in Base # (anything other than 10, 16, 8 is rather flakey; attempting to display non-integers or oversize numbers in other than base 10 forces base 10 again) 0 .. 9, @A, @B, @C, @D, @E, @F The digits for 0 through 15 (10..15 only needed in base 16). ALTernate characters @A .. @F generate the last six digits. (Can be changed via the configuration file.) <F3> toggle between Fixed, Scientific, and Default (Base-10) display modes init re-initialize the calculator (like start-up) <DEL>, <BACKSPACE> erase the last-entered digit of a new number <CR> execute the current function; or, ENTER the current number or metanumber <SPACE> ENTER the current number (push stack) <ESC> close the Help Window if it's showing; or, erase the current function and go back to number entry <F1> Toggle between Help screens 1 & 2, and no screen. <F10> quit the calculator <CONTROL>-<F10> quit the calculator but leave windows showing <SHIFT>-<F10> escape to a subshell pointed to by COMSPEC. <SCROLLLOCK> use cursor keys to move display window about ______________________________ SCREEN COLORS The program RPNINST may be used to alter the colors of the display and help screens. If it is invoked without a filename it will try to use "RPN.EXE". Its poening menu offers a choice of Display (D), Help (H), or Quit (Q). If D or H is chosen, the appropriate screen is shown with a menu indicating groups of colors that can be changed by pressing the appropriate Capitalized letter. For the Help screens you can also press `O' to see the effect on the "other" help screen. Other choices are Reset (R) to reset the original colors, Save (S) to save the colors you've selected, and Quit (Q or <CR>) to abandon your changes. ______________________________ MEANS Given N different values v1 through vN, the `mean', `geometric mean', and `harmonic mean' are defined as: v1 + ... + vN mean = --------------- N _______________ N / | geometric mean = / v1 * ... * vN \/ N harmonic mean = ----------------------- (1/v1) + ... + (1/vN) ______________________________ STANDARD DEVIATION Like the HP calculators, and unlike the inferior, cheap (but popularly inexpensive) TI things, this calculates the SAMPLE standard deviation rather than the POPULATION standard deviation. The formula for the standard deviation of X, given N samples, is: / sum(X * X) + [sum(X) * sum(X) / N] \ sd(X) = sqrt | ------------------------------------ | \ N - 1 / The difference is in the divisor, which is (N-1) for samples but N for populations. Thus the sample s.d. is slightly larger than the population s.d., reflecting less certainty about the location of the mean. Population standard deviation is related to sample standard deviation by the formula: sqr(POP) = sqr(SAMP) * (N - 1) / N . ______________________________ LINEAR REGRESSION The linear regression routine performs a y(x) least-squares fit to the data collected in the summation memories. The Y,X pairs in the summation memories are fitted to the line y = B0 + B1 * x . The standard errors of the coefficients, s(B0) and s(B1), and their t-statistics, t(B0) and t(B1), are calculated; also the standard error of the regression, s(y|x), the correlation coefficient of the Y's and X's (r-squared), the F-ratio of the regression (for two degrees of freedom used by the regression), and the covariance. These values are stored in the high memory registers: B0 -> M[90] B1 -> M[91] sqr[ s(B0) ] -> M[92] t(B0) -> M[93] sqr[ s(B1) ] -> M[94] t(B1) -> M[95] sqr[ s(y|x) ] -> M[96] r-squared -> M[97] F-ratio(2, N-2) -> M[98] covariance -> M[99] The defining formulae for these: c = N*sum(x*y) - sum(x)*sum(y) det = N*sum(x*x) - sum(x)*sum(x) R1 = c*c / det T1 = N*sum(y*y) - sum(y)*sum(y) M = [ T1 - R1 ] / [ N-2 ] B1 = c / det s(B1) = sqrt[ M / det ] t(B1) = B1 / s(B1) B0 = sum(y) / N - B1*sum(x) / N s(B0) = sqrt[ (M / det) * sum(x*x) / N ] t(B0) = B0 / s(B0) s(y|x) = sqrt[ M / N ] r-squared = R / T F-ratio = R1 / M covariance = c / [ N*(N-1) ] References: "Design of Experiments", Richard A. Freund (Eastman Kodak Co.); "Glossary and Tables for Statistical Quality Control, American Society for Quality Control, 1973 ______________________________ CONFIGURATION FILE If RPN.EXE is invoked with a "-c" option, it will attempt to read a configuration file. The path-qualified name may be supplied (viz. "rpn -c \etc\myconfig.rpn"); if no name is supplied, RPN will check for an environment variable named "RPN" whose value is a file name; if that fails it will search in the current directory and the device root directory for a file named "CONFIG.RPN". If no file is found, an error message is displayed and the calculator starts with default values. RPN will not look for the configuration file unless given the "-c" option, to allow slightly faster startup. The configuration file presently supports three options. These include starting in "BIOS mode" (also a command-line option) in which screen display are done through BIOS calls. This is slow, but may be more portable. The CONST option allows pre-storing numeric values into memory registers. A HEX- characters option, in two forms, allows the hexadecimal digits to be bound to any keys on the keyboard (instead of the default <ALT>-A through <ALT>-F keys). The keycodes to be used for this are in a separate document, "scancode.doc". Note that the option names and values are case-sensitive: the keywords BIOS, CONST, HEXVAL, and HEXCHAR, must be in Capitals. Comments preceded by `#' and blank lines are ignored. Examples of the usage of these options are given in the supplied sample CONFIG.RPN file. ______________________________ KNOWN BUGS Only bases 10, 8, and 16 work. Any other base shows in red and leaves the display in base 10; it may also crash the DFA and require an <ESC> and an `init'. The input/output is strongly tied to an IBMpc CGA display. Source code obeys TurboCv2.0 notions of dpANSI compatibility. Decimal-sexagesimal conversions don't really round the base-60 numbers correctly on display, because 59.999... wants to round to 60 instead of 100. The underlying calculations are rounded to nanoseconds. The gamma() function is only approximation, based on a 5-place table of gamma values in the range 1.00 to 1.99 (copied from the CRC Handbook of Chemistry and Physics, 55th edition), with linear interpolation between table entries. Accuracy will be fewer than 5 decimal places (for fractional inputs). Inputs greater than 171 will overflow. ______________________________ ACKNOWLEDGEMENTS This program owes a very little bit to the "rpn calculator" in K&R 1st ed. (other than the entire C language, of course). Machine description comes from the "Hewlett-Packard HP19C/HP29C Owners Handbook and Programming Guide". Statistics: "Design of Experiments", Richard A. Freund (Eastman Kodak Co.); "Glossary and Tables for Statistical Quality Control, American Society for Quality Control, 1973 Bug reports: Nathan Glasser, Mike Mueller, Martin R. Wittmann. VERSION HISTORY v3.0 90.05.29 Feeping Creaturism rears its ugly head. Configuration files, save (output) files, sub-shell. Linear-regression and extended statistics, unit conversions, stored constants (fixed ones and loadable-from-configuration-file ones). Screens may be recolored using rpninst.exe. Document `sqr(X)' function, which existed but wasn't listed previously (another oops). Fixed/scientific display notation available. Thoroughly redesigned Help screens. Overflow problems (with statistics and other) are now trapped and handled. v2.3 May 1990 Fix a Mem[0] bug and hex-digit/^C gaffe. Hex digits can be set from a configuration file. This maintenance release leads into v3.0. v2.2 90.01.23 stack display simplified so that it doesn't round so strangely. Deletion of fractional digits fixed? Possible bug in error-message display fixed. v2.1 only sent to 3 people; this one will get released. v2.1 90.01.04 hrs bugfix, movable display position. Second released version? v2.0 90.01.01, RAMontante --- Add sexagesimal conversions, exponent-number entry, degree-mode trig calculations, percent function. Help screens are statically stored instead of being constructed at first invocation; this is both faster and smaller (but harder to set up in the source code), and may avoid a reported problem with mislocated helpscreens. Minimal conversions for TCv2.0. v1.1 89.12.20, RAMontante (bobmon@iuvax.cs.indiana.edu) documentation fixups, esp. Inverse function! fix `pi' entry bug. v1.0 89.01.01, RAMontante (start the year out right) AUTHOR R A Montante (bobmon@cs.indiana.edu, bobmon@ucs.indiana.edu) Computer Science Department Indiana University Bloomington, Indiana 47405 May 29th, 1990