Club Amiga de Montreal - CAM/CAM_CD_1.iso/files/306.lha/RPSC/RPSC.doc

Text File | 1980-12-05 | 14.4 KB | 405 lines

                              R P S C     1.1

                 Reverse   Polish   Scientific   Calculator


                             Copyright    1989

                                    by

                              Gary   Teachout




      A programable RPN calculator in the Hewlett-Packard tradition




 Contents:

   Introduction
   Reverse Polish Notation
   Programs and User Defined Functions
   Summary of Functions and Operations
      Stack
      Modes
      Storage
      Arithmetic
      Programing
      Control
      Files
   Errors and Messages
   Freeware


 Introduction:

      RPSC is a programable reverse polish notation calculator for
   the Amiga which may be run from the Workbench or the CLI.
   It suports operations with real numbers, complex numbers,
   matrices, and 3-D vectors. As well as storage and recall of
   labeled variables. Data and programs may be saved to, loaded from,
   or writen as ASCII text to AmigaDOS files. It uses the Intuition
   user interface of Gadgets and Menus. The numeric keypad as well as
   the letters and symbols to the right of each function gadget
   may be used as keybord alternatives.

      RPSC may be terminated at any time by pressing the escape key
   or selecting the Esc button.


 Reverse Polish Notation:

      In Reverse Polish Notation ( RPN ) also called postfix notation
   numbers are specified before the operation to be performed.
   For example the sum of five and seven could be written:

               5  +  7           algebra or infix notation.
               +  5  7           polish or prefix notation.
               5  7  +           reverse polish or postfix notation.

   The advantage of RPN is apparent in the more complex example:

               ( 141 + 15 ) / ( ( 3 * 11 ) - 21 )         algebra
               141  15  +  3  11  *  21  -  /             RPN

   To perform this on an algebraic calculator requires that you
   store the result of some operations while performing others.
   On an RPN calculator it may be keyed in as is using the ENTER
   key or an operation to separate numbers:

         1 4 1  ENTER  1 5  +  3  ENTER  1 1  *  2 1  -  /

   The result ( 13 in this case ) is displayed and is available
   to further operations.

      RPSC stores numbers in a group of four registers known as
   the "stack". The registers are labeled "x", "y", "z" and "t".
   Each register may contain a real number, a complex number, or
   the descriptor of a matrix or vector. Input numbers are keyed into
   the x register. A push operation loads the x register and copies the
   previous contents of each register up to the next register. The
   previous contents of the t register are discarded. A pull or pop
   operation removes the contents of the x register and copies the
   previous contents of each register down to the next register. The
   t register is unchanged. Inputs to each operation are popped off the
   stack, the operation is performed, and the result is pushed back on
   to the stack.


 Programs and User Defined Functions:

      Almost any sequence of operations may be entered as a program.
   Programs must begin with a label and should end with a return.
   The usual way to run a program is gosub followed by the label of the
   program.

      User defined functions are programs that accept a single input and
   return a single result. User defined functions can expect the stack
   to be filled with the input variable. Such programs may be evaluated
   ( Extra 0 ), graphed ( Extra 1 ), numerically integrated ( integ. ),
   or numerically solved ( solve ). These operations first fill the stack
   with the input variable then call the function as a subroutine.


 Summary of Functions and Operations:

   Stack:

      Enter       Push x make room for next input.
      E  exp      Enter exponent
      E  im       Enter imaginary portion of complex number.
      <---        Clear x make room for next input.
      pop         Pop x off of stack and discard.
      up          Rotate stack up.
      down        Rotate stack down.
      x <-> y     Swap x and y.
      a <-> b     Swap real and imaginary portions of x.

   Modes:

      degrees     Interpret angles as degrees.
      radians     Interpret angles as radians.

      fixed
         1 - 9    Display numbers in fixed point notation.
      sci
         1 - 9    Display numbers in scientific notation.
                  1 - 9    Number of digits precision.

      complex     Initiate complex mode. Show complex stack.
      real        Terminate complex mode.

      fast        Speed up programs by turning off the display.
      slow        Terminate fast mode. Display normal.

      program     Enter or exit program mode.

   Storage:

                  Any button with a letter to its right may be used
                  as a label to identify a variable.
                  Storage operations must be followed by a label.

      dim         Define variable as matrix of dimension x * y.
                  If x = 0 or y = 0 undimension.
      rcl  M      Recall Matrix and push descriptor on to stack.
      result      Specify variable to receive matrix result.
      store I     Store x in matrix index.
      rcl   I     Recall matrix index into x.
      store       If label specifies a matrix store x into the
                  indexed element then increment index.
                  If not a matrix store x at label.
      rcl         If label specifies a matrix recall the
                  indexed element into x then increment index.
                  If not a matrix recall from label into x.
      rcl-(I)     If label specifies a matrix decrement index then
                  recall the indexed element into x.
                  If not a matrix recall from label into x.

   Arithmetic:

      +           Add numbers or like matrices.
      -           Subtract numbers or like matrices.
      *           Multiply numbers or compatible matrices.
                  Scale matrix or vector.
      /           Divide numbers.

      int         Integer portion of real x.
      frac        Fractional portion of real x.
      abs         Absolute value of real x.
                  Magnitude of complex, vector, or matrix.
      chs±        Change sign of real x.
      mod         Modulus remainder after division.
      %           Percent.
      x !         Factorial x or Gamma of ( x + 1 ) .
      1 / x       Invert.
      x 1/2       Square root or x to the power 1/2.
      y 1/x       x root of y.
      x ²         x squared.

      sin         Sine.
      cos         Cosine.
      tan         Tangent.
      sin -1      Inverse Sine.
      cos -1      Inverse Cosine.
      tan -1      Inverse Tangent.

      sinh        Hyperbolic Sine.
      cosh        Hyperbolic Cosine.
      tanh        Hyperbolic Tangent.
      sinh -1     Inverse Hyperbolic Sine.
      cosh -1     Inverse Hyperbolic Cosine.
      tanh -1     Inverse Hyperbolic Tangent.

      y^x         y to the power x.
      e^x         e to the power x.
      10^x        10 to the power x.
      logx y      Base x Logarithm of y.
      loge x      Base e Logarithm of x. Natural Logarithm.
      log10 x     Base 10 Logarithm of x. Common Logarithm.

      random      Random number between 0 and 0.999...
      e           Natural Logarithm base  = 2.7182818...
      pi          Pi = 3.1415926...

                  These must be followed by a digit.

      Vector      A vector may be any three element matrix.
                  An orthogonal basis is a three by three matrix where
                  each row is a perpendicular unit vector here
                  labeled I, J, and K.
         0        Vector sum           y + x.
         1        Vector difference    y - x.
         2        Vector product       y dot x.
         3        Vector product       y cross x.
         4        Angle between two vectors.
         5        Project vector y into basis x.
         6        Rotate y basis vectors I J angle x.
         7        Rotate y basis vectors J K angle x.
         8        Rotate y basis vectors K I angle x.
                  Rotate operations act directly on the basis y.

      Matrix
         0        x = transpose of x.
         1        Result = transpose of x.
         2        x = inverse of x.
         3        Result = inverse of x.
         4        x = determinant of x.
         5        Result = copy of x.
                  All of these accept one matrix as input.

      Extra       The first two of these must be followed by the label
                  of a user defined function.
         0        Compute user defined function F(x).
         1        Display graph of user defined function.
                     top of display            = t
                     bottom of display         = z
                     left edge of display      = y
                     right edge of display     = x
         2        Time in hours since midnight.

      Convert
         0        Polar coordinates to rectangular.
         1        Rectangular coordinates to polar.
                  In polar coordinates x = magnitude y = angle.
         2        Degrees to radians.
         3        Radians to degrees.
         4        Gradians to radians.
         5        Radians to gradians.
         6        Hours to hours minutes seconds.
         7        Hours minutes seconds to hours.

   Programing:

                  Programs in RPSC consist of almost any sequence of
                  key strokes. While in program mode all but the
                  following will be recorded as part of the program.

                  The up and down arrow keys may be used to scroll
                  through the program. Shift up and down arrow keys
                  scroll ten lines at a time.

      program     Enter or exit program mode.
                  When you exit program mode the program is scanned
                  for labeled entry points.

      forward     Scroll forward through program one line.
                  Same as curser down.
      back        Scroll backward through program one line.
                  Same as curser up.

      del         Delete line from program.
      clr pgm     Delete entire program.

   Control:

      label       Mark entry point in program.
                  Must by followed by a valid label.

      goto        Jump to entry point. Must by followed by a valid label.
                  May be used to start a program.

      gosub       Subroutine call. Must by followed by a valid label.
                  May be used to start a program.

      return      Return from subroutine.

      stop        Terminates program execution.

      integ.      Numerical integration of a user defined function over
                  the interval y to x. Must by followed by a valid label.
                  Results
                     x = integral
                     y = uncertainty

      solve       Numerical solve. Find a root of a user defined function.
                  Must by followed by a valid label.
                  Inputs
                     first guess       = y
                     second guess      = x
                  Results
                     x = root
                     y = F(x)    If y is negligible or zero then x is
                                 a root. If not then x is where  | F(x) |
                                 has a local minimum.

                  If these test operations fail, the next operation
                  will be skipped. If they are true, they have no effect.

      set   f
         0 - 7    Set flag number 0 - 7.
         9        Set user program error.
      clear f
         0 - 7    Clear flag number 0 - 7.
         9        Clear user program error.
      f ?
         0 - 9    Test flag number 0 - 9. Flags 0 - 7 same as above.
                  Flag number 8 tests for complex mode.
                  Flag number 9 tests for user program error.

      x <> 0      x not equal to 0.
      x > 0       x more than 0.
      x < 0       x less than 0.
      x >= 0      x more than or equal to 0.
      x <= 0      x less than or equal to 0.
      x = y       x equal to y.
      x <> y      x not equal to y.
      x > y       x more than y.
      x < y       x less than y.
      x >= y      x more than or equal to y.


   Files:

                        The File Access menu contains the following
                        operations. They present a file name requester
                        where you may enter a file name or cancel the
                        operation. Operations that write ASCII text
                        may be directed to a printer by entering PRT:
                        as a file name. All of these may be included
                        in programs, however, those that load programs
                        will be ignored at run time.

      join program      Add program from file to end of existing
                        program.

      load program      Load program from file writing over existing
                        program.

      load x            Load x register from file. If file contains
                        a matrix load result.

      load storage      Load all storage variables from file.

      save program      Save copy of program.

      save x            Save copy of x register.

      save storage      Save copy of all storage variables.

      list program      Save program as ASCII text.

      write x           Save x as ASCII text. If x is a matrix each
                        element will be separated by a comma ","
                        and a line feed. Such a list may be pasted
                        into documents and programs.

      write strip       Opens a file and begins writing an ASCII
                        record of each operation that follows.

      disable strip     Closes file opened by write strip.


 Errors and Messages:

      Messages appear in the screen title bar and remain until
   another operation is performed.

      Numerical errors such as "divide by zero" are not fatal
   and will not interfere with program execution. The results
   however, may be undesirable.

      Nonsense errors such as "incorrect type" ( example: trying to
   take the integer portion of a matrix ) or "file error" ( file not
   found or volume is full ) are fatal and will stop a program.

      User program error ( set f  9 ) is not displayed until the
   end of a program.


 Freeware:

      You are welcome to copy this program for all of your friends.


            Gary Teachout
            10532   66 place   W
            Everett   Wa   98204