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Text File | 1990-11-21 | 33.4 KB | 973 lines

SJ Scientific presents an RPN based scientific calculating tool R RRRR PPPPPP NN NNN R R P P NN N R R P P N N N SJ . RRRRR PPPPP N N N R R P N N N R R P N N N R R P N NN RRR RR PRP NNN NN Written by J.I. Landman Copyright 1989,1990 SJ Scientific (SJ Scientific is a partnership wholly owned by Sofia Villanueva and Joseph I Landman, whose purpose is the dissemination of tools useful for students/professionals using personal computers) Table Of Contents: ++++++++++++++++++ Page Description ---- ----------- 3 Introduction 4 Program Description 5 System requirements 5 Legal Stuff 6 A Note to New Users 8 Starting Out 8 Program Usage 11 Function List 15 Ordering Info Introduction: ============= RPN is a calculating tool written by J.I. Landman to be used primarily by scientists and engineers. RPN is basically a calculator, with quite a bit of power. RPN is a useful and powerful tool for those who regularly use Hewlett Packard calculators (such as the HP-42S, after which RPN was modeled), and wish a similar amount of functionality on their PC's. RPN is rather bland looking when first invoked. But looks aren't important. I am afraid that I am more interested in the utility of a tool than its appearance, as I would hate for my wonderful creation to sit unused but beautiful upon someone's machine. This might be changed in the future. But for the moment, I have attempted to make RPN be as user friendly/fault tolerant as possible. As well, RPN can do things that few other programs for a PC can do. RPN handles complex numbers in a transparent fashion, indeed it is intrinsically a complex number calculator. With 1 or 2 noted exceptions, ALL the functions that normally operate upon the set of real numbers have been extended and researched (in my handy dandy copy of "Handbook of Mathematical Functions" Abramowitz and Stegun) to deal with the complex plane. I am also intrigued by the possibility of a 1 word synonym replacing several commands. So I have included this within the program. The Synonym as it is implemented, is a wonderful thing. one may store useful numbers within it, as well as commands. More on this later. I have found the stack paradigm to be a useful tool in my calculating tasks, so I have implemented a simple stack of complex numbers, 16 entries deep. (8 of which are visible on screen). In all fairness, this calculator reflects my prejudices about computation in general. I find it suits most of my needs very well (I am a graduate Physics student). I hope that it will suit other physical scientists/researchers/engineers/students as well. Please do feel free to correspond with me about what you like or dislike, and what features you would like to see. I am very amenable to suggestions for improvement of this tool. Note: Within this document and my program, I make liberal use of the word RPN. I have explained the meaning of RPN, but I know not whom owns the copyrights (if any) to that word idea, etc. However... I do also use the words NOS TOS ... . These are ideas that I found within my HP-15C manual. Thus my very limited research leads me to believe that I should cite Hewlett Packard as the holder of copyrights for those ideas. Indeed the very inspiration for this program was my brand new HP-42s calculator. I very much wanted a similar program on my PC. So I wrote one. So I wish to thank HP for the terminology TOS,NOS, and for their marvelous calculating tools. (HP-42s, NOS, TOS are copyrights of Hewlett Packard Corp) What RPN was written in ======================= RPN is written in MicroSoft QuickBasic version 4.5 The choice of this language was rather simple, BASIC though scoffed at by so called professional programmers, is a powerful language. (since QB is NOT available on Vaxen and IBM mainframes I am beginning the process of porting this program to fortran, though I am investigating recoding it to live happily on the Vax) As a result of its beautiful debugging [Quickbasic] environment, I have been able to test the program to a very fine level. For each function I have added, I have checked MANY values in the real and complex plane against what is printed in A&S, and as well, against my HP-42s. I had found problems with several algorithms in A&S (well I wrote the code...), so I reworked the math as to correct them. There may yet be little critters hiding somewhere, but I have not found any recently... (yes I have been looking). I would be cautious in general about using functions near the limits of their domains. For example, from L'Hopitals rule we know that sin(x)/x goes to 1 in the limit of x approaching 0. RPN craps out around x=10^(-170) or so (thats 10.0d0**(-170) for the more fortranesq reader). But those who use RPN are quite familiar with the idea that one should be careful about dividing by very small numbers. For those interested, I am relying upon the built in emulator library, and thus have not coded the lower level function calls myself. I will try to put in taylor and asymptotic expansions in the near future, in an effort to increase the accuracy. I have replaced the old magnitude function to deal with the case of one component of the complex number being much larger than the other. I use an exact expression for 1 case, and a taylor expansion for the other. This gives more exact results in general. SYSTEM REQUIREMENTS =================== I recommend first of all some sort of IBM PC compatible computer. I have no idea whether this or any program compiled in QB will work on every compatible, or PC emulator (eg MacPC etc). I wrote this on my "souped up" PC (well, I have an 8087...) You will need 1 or more disk drives. A hard disk is fine, or a ram disk, etc. (I use my hard disk) A note: The program only reads or writes disks during diary operations. You will need some sort of display and adapter (not necessarily graphics). Most definitely you will need a keyboard, some electric current, and the desire to play with this program. Once you have this you are all set. Please do note, I will and I do assume a certain level of knowledge in mathematics and the use of PC's. The software can use the 8087 numeric coprocessor, or it will do a very nice job of emulating it if you do not have it. RPN needs at least 160K of main memory (RAM). It requires DOS 2.1 or higher (my machine uses DOS 3.3, but I used no advanced DOS functions). It does require an 80 column display so it will run on any of MDA,HGC,CGA,EGA, or VGA (my VGA works very well with it) You can see how versatile this program is already! A Note to new users. ____________________ Scope and Domain of program =========================== The source code is not available, and the copy of the program you have is an unregistered evaluation copy. I place this program into the public domain, under the "Shareware" concept. That is if you find this program of utility for you or your work, then please do read on, otherwise, feel free to pass this along to several friends who may find some use for this sort of tool. I do encourage you to upload this to BBS's far and wide, intact (eg the way you downloaded it from a BBS, received it from a friend, etc). The scope of the program is that of an extensible complex number calculator. I will be adding features such as integration by various means, differentiation, etc, as soon as I recode this into fortran. It is USER EXTENDIBLE by using the SYNONYM command. This is EXTREMELY powerful (caps for emphasis!). GENERAL INFORMATION ==================== (and legal stuff) i) Me I am a graduate student at Wayne State University studying Physics. I am working toward my PhD. (I have my masters as of June 1990). Being a graduate student, I am living on the miserly pittance given by the university for many hours of hard labor. Thus the MANY months of development time I have put into it are worth quite a bit to me, and they should be to you as well. So If you need to contact me for ANY reason... My school mail box J. Landman Graduate Student, Physics and Astronomy Dept, Physics Bldg, Wayne State University, Detriot, MI 48202 (313)-425-5159 (voice) landman@msupa.bitnet landman@msupa.pa.msu.edu 07480jln at MSU 07480jln@msu.bitnet msuhep::landman ii) You You are free to use and copy this program and documentation, provided you distribute all the original files, and make no alterations to them. If you wish to use this in a corporate, or laboratory environment, you must arrange for a site license from SJ Scientific. The rates are: $12.50 for the first 2 computers. $10 for each additional computer over the initial 2. (considering the cost of a new calculator this is quite good) If you find this program to be of utility for your work, I would encourage you to contribute to my efforts, and and register this copy of RPN, as your conscience would bother you for the rest of your days if you did not... If you would be interested in receiving the latest version of RPN, please send me a blank formatted disk, a large Self Addressed Stamped Envelope, and $10.00 in the form of a check or money order (to cover my overhead, $12.00 if you do not have a disk, $15.00 if you do not have an envelope either). Obviously, I will register you as a user. iii) Registration If you wish to register yourself as a user of the program, then please send me your name, address, phone number, and $12.50. This entitles you to the latest version of RPN. If you are seeking a site licence, then you must register each copy of the program as noted above. (see "ii"). I will attempt to provide upgrades at more or less a quarterly basis. It may be more frequent, it may be less, depending upon my schedule of classes, research, etc. I make no guarantees as to the frequency or number of updates. iv) Where I am going with all of this I am targeting this program for the people studying physical sciences and related topics. I am VERY open to suggestions. So please feel free to comment. If you find or write useful synonym libraries (or useful diary files), I would be happy to include them in the utility files of the distribution. v) Liabilities See the other document file within this package. Now for useful things... STARTING OUT (running the program) ============ Somehow place RPN into the default directory. This can be accomplished any number of ways. for a hard disk system, if the program is in C:\RPN type CD \RPN <enter> for a floppy drive system, first make sure you have RPN on the diskette in the default drive. for example if RPN is on drive B, type B: <enter> Now type RPN <enter>. Where <enter> is the enter/return key. You are now in the program. USING RPN ========= 1) How to enter expressions RPN is a notation developed by a Polish Mathematician in order to simplify computation and order of operations. It is also called postfix by computer science types. Hewlett Packard calculators are famous for their implementation of postfix. We are used to a notation called infix where operators (such as +,-,/,* etc) are placed between 2 numbers. For example 1 + 1. As well, on most infix calculators (such as TI, Panasonic, Sharp, etc) you may form very complex expressions with the use of parenthesis'. For example ((( a + b )^(3/2))(F(x)) To enter the equivalent RPN expression, you would enter the following line at the prompt. a b + 3 2 / ^ F(x) * <enter> ( <enter> is the enter or return key on your keyboard ) This has a simple interpretation. Read from left to right. Push numbers onto the stack, and operators operate upon the first 2 elements of the stack. So "a b +" pushes a, then b onto the stack. Then it applies the addition operator which takes the stack top (TOS) and adds it to the next element in the stack (NOS). Then it pops the stack, and replaces the top of the stack with the sum that it computed. "3 2 /" pushes 2 then 2 onto the stack, then divides the NOS (the 3) by the TOS (should be 2). " ^ " takes the next on stack to the power of top of stack, and pops the stack. "f(x) *" pushes f(x) onto the stack, then multiplies to produce the final result. Do note that this is NOT the only way to use the RPN notation for this problem. For example, let us assume that x,y,z,t are synonyms for certain numbers. Suppose I had to add all of the numbers together for my operations. We could type x y z t + + +<enter> or x y + z + t +<enter> or x y z + + t + Polynomials are rather easy to enter using Horners rule. 2 3 4 let f(x)=a + a * x + a*x +a *x + a *x 0 1 2 3 4 we can rewrite this as f(x)=a + x*(a + x*(a + x*(a +x*a ))) 0 1 2 3 4 or using RPN a4 x * a3 + x * a2 + x * a1 + x * a0 + by now you have the basic idea! COMPLEX NUMBERS: RPN handles complex numbers in a transparent fashion. To enter complex numbers, note the following: Let a,b be real numbers. a complex number is entered into RPN as follows: a+bi "i" is the indicator of a complex part of a number. Allowable variations are as follows a or b: Real numbers ai or bi: Imaginary numbers a-bi: complex numbers -a+bi: " " -a-bi: " " example: to get 0+1i (better known as i) as the display, type -1 sqrt <enter> or 1i to enter 1+5i + 3-4i type 1+5i 3-4i + <enter> Editing: -------- I have written a simple line editor for RPN input. It allows the arrow, function, escape, insert, and delete keys to be used. Pressing the up or down arrow after some RPN commands have been entered, scrolls back through the command buffer, also 16 elements deep. The Insert and delete keys perform as expected, and the backspace functions as a true backspace. The left and right arrows move you around on the command line to allow corrections etc. The escape key erases the current command input line, or while executing long synonyms or files, terminates their execution. The function keys perform the indicated operations. I like it (and it was one bear to debug!), and I hope you do as well. Error Messages: --------------- I worked awful hard to get useful error messages to the user. The error handler reports the error number and the problem (If it understands it...) So far I have been successful at identifying what errors are caused by what process. If you encounter one that simply gives the error number and no message, then please let me know the circumstances of the problem, that I may investigate. The System is very fault tolerant. 2) FUNCTION LIST USAGE: simply type the name, and unless otherwise noted the function will act on the top of the stack. The results are left in the Top Of Stack (eg TOS). (commas separate synonymous commands) a) Basic math operations (C# = Complex number, R# = Real number) ===================== (TOS = Top Of Stack, NOS = Next On Stack) this notation is from the HP 15c users guide published by HP. (tm Hewlett Packard). The notation is compact and convenient. operator description of operation -------- ------------------------ + addition (TOS+NOS) - subtraction (NOS-TOS) * multiplication (TOS*NOS) / division (NOS/TOS) ^ exponentiation (NOS^TOS) ! factorial (TOS) !! double factorial (TOS) 1/X,INV inversion (TOS) ABS Absolute magnitude (TOS) CONJ,~ complex conjugate (TOS) EXP exponentiation (TOS) LN natural log (TOS) LOG base 10 log (TOS) MAG magnitude of C# (TOS) ARG argument of C# NEG,-1*,NEGATE,NEGATIVE negate both imaginary and and real parts (TOS) RNEG negate real part (TOS) SQRT,ROOT square root (TOS) SWAP swap TOS and NOS CSWAP swap the real and imaginary parts (TOS) FIX set the number of digits in the decimal b) Trigonometric Operators ======================= operator description -------- ----------- ACOS,ARCCOS Inverse cosine (TOS) ASIN,ARCSIN Inverse sine (TOS) ATAN,ARCTAN,ATN Inverse tangent (TOS) COS,COSINE cosine (TOS) SIN,SINE sine (TOS) TAN,TANGENT tangent (TOS) c) Hyperbolic Operators ==================== operator description -------- ----------- ACOSH,ARCCOSH,INVCOSH Inv Hyperbolic cosine (TOS) ASINH,ARCSINH,INVSINH Inv Hyperbolic sine (TOS) ATANH,ARCTANH,INVTANH Inv Hyperbolic tangent(TOS) COSH Hyperbolic cosine (TOS) SINH Hyperbolic sine (TOS) TANH Hyperbolic tangent (TOS) d) Constants ========= operator description -------- ----------- a0,ab,abohr Bohr Radius in meters c speed of light in m/s e electronic charge in coulombs ev Electron Volts in c/m h Plancks constant in J s hbar Diracs constant (h/(2 pi)) pi 3.14159265.... euler Eulers constant e) System Commands =============== operator description -------- ----------- DIARY saves a diary of commands to disk QUIT,EXIT terminate session and return to dos READ DIARY filename.ext reads a diary file from disk of the name filename.ext REFRESH Toggles the refresh flag to allow/disallow refreshing the stack display after every operation. The default is to see every operation. This is a bit slow, but it is fun to see. SYN,SYNONYM command synonym creates a synonym in memory, for the entry 'command'. When the parser encounters the entry 'command', it replaces it with the string of operators or numbers found in the synonym. eg SYN F sqrt sqrt defines F as the 4th root YOU MAY OVERRIDE THE INTERNAL FUNCTIONS WITH A SYNONYM!!!! SYN- removes a synonym from storage. STORE,STO synonym element_of_stack will store the contents of stack pointed to by the last number into the synonym. If synonym does not exist, then it is created. eg STORE x 3 will store the 3rd element of the stack into synonym x. To use the value stored into x, just type x where you need it!!! UNFORMAT toggles the formatted and unformatted modes of numeric display. to force 7 digits of decimal display from the unformatted display, you must do the following. UNFORMAT FIX 7 to flip back to an unformatted display, just type the unformat command. 3) DESCRIPTION OF SYSTEM OPERATORS Before I get deeply involved into this description, I must make a note to you that all of the numerical operators with the exception of the Summation operator, are operable on the entire complex plane. This obviously includes the real axis, and imaginary axis. The other rather obvious exception to this is the inverse of 0 (or 0+0i). I will work on some method for properly handling infinities as they crop up. Constants push themselves onto the stack. They are usually real. DIARY: ====== Diary saves every command that you type in to an ascii file of your own designation. These files are editable by any word processor capable of reading ascii files (obviously). You may change them as you wish, to include more or fewer operations. I would strongly advise against including any system level commands with the exclusion of SYN, or REFRESH. EXIT or QUIT: ==== ===== EXIT or QUIT are very simply the methods of leaving RPN to DOS. There is no difference between then, just a matter of preference as to what you use. READ DIARY filename.ext: ======================== READ DIARY filename.ext reads the diary files created by DIARY, or by your own word processor. The files are simply series of operators, numbers or commands. As each line of the file is read, it is displayed at the bottom of the screen (where you normally enter the commands). This simple interpreter will be extended in future releases. SYN or SYNONYM command synonym: === ======================== SYN or SYNONYM command synonym places the single word command into the synonym look up table. When the parser encounters this word command, the parser replaces the word command by the string synonym. If entered on one line, then the synonym is assumed to be the rest of the line after command. An example. SYN ADD + will put the command ADD in the synonym list. To use this new synonym, we simply include it in the input line. For example... 1 1 ADD will be interpreted as "1 1 +" by the parser. Synonyms may be very complicated. For example. SYN F LN 1/X NEG EXP (this function F has the interesting property that F(F(x)=x, Synonyms may contain numbers and other synonyms. WARNING!!! DO NOT ATTEMPT TO MAKE RECURSIVE DEFINITIONS OF SYNONYMS!!!! eg do NOT attempt the following unless you wish to terminate the execution of the synonym by pressing <escape>. eg: SYN R1 1 + R1 This does the following. pushes 1 onto the TOS. Adds the NOS to TOS and pops the stack, placing the sum in TOS. Then the parser expands the synonym R1 (eg self referent) and executes that... ad nauseam. This will simply never stop executing until you press the escape key. The length of synonyms should be kept to 80 operators or less. If you have a need for more, please send me a letter, and I will recompile the parser to accommodate it. SAVE object filename.ext ======================== This command saves the object to filename.ext Object can be the 1st 3 letters of STAck, SYNonyms, or BOTh. This command writes a diary file out to disk, and can be read back in to restore a session by using READ DIARY filename.ext. NOTE: In the event of file name collision, RPN will ask you if you wish to Append to the existing file of the same name you had specified, or simply overwrite it. If you wish neither, simply press enter. Append is much safer than Overwrite, in that you may recover from mistakes. tm=trademark (1) HP42s,HP15c, etc tm Hewlett Packard Corp, (2) TI55 etc tm Texas Instruments Corp. (3) Panasonic tm Panasonic Corp. (4) Sharp tm Sharp Ltd. Ordering Info Name:_____________________________________________________ Company:__________________________________________________ Title:____________________________________________________ Dept:_______________________ office num:____________ Street:___________________________________________________ City:_______________________ State:_____________ Zip:_________ st I would like to register _____ copies of RPN at $12.50 for the 1 2, and $10 for each additional copy. I have enclosed a check or money order for $______ made out to Joseph Landman, or Sofia Villanueva. Mailing address: Physics and Astronomy Building, 666 Hancock Avenue, Wayne State University, Detriot MI 48202 Comments: (please include so that you will help us to improve our product, and better meet the needs of our users!)