Turnbull China Bikeride/Turnbull China Bikeride - Disc 2.iso/STUTTGART/LANG/ASSEMBLER/FLOATENCODE/<tarZ$use>/files/floating2/Article3

Text File | 1989-05-14 | 8KB | 397 lines

    Getting the Point......in BASIC





    (c) Copyright TJ Chappell April 1989.



         Acorn's latest version  of BBC BASIC has  improved many of

    the  features   of  previous   versions  and  added   many  new

    facilities.  However, the latest version  is still limited by a

    maximum of  9 decimal places  and maximum exponent of  only 38.

    These limits are normally acceptable for most users but what do

    you  do if  you  require  more accuracy  or  a  wider range  of

    numbers?



         Until now the only possibilities  were to use a scientific

    calculator and enter the numbers into PRINT statements or write

    a machine code  program to use  the facilities of  the floating

    point unit.  Neither of these options offer a complete solution

    to the BASIC programmer.



         The solution offered here removes the need to learn how to

    program the floating  point unit directly or  press any buttons

    on  a  calculator.  The  program  is  presented as  a  function

    library which can  be installed into the machine  in the normal

    way using the  INSTALL, LIBRARY or APPEND  command as required.

    It also relies upon the floating point emulator being installed

    as well.



         Since BASIC  would round  numerical variables to  suit its



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    own  precision  it  is  necessary that  all  extended  accuracy

    numbers are  stored in string  variables.  The numbers  are all

    stored in the following format :



         +/-m.mmmmmmmmmmmmmmmmmm E+/-eeee



         This  leads to  numbers  with a  precision  of 18  decimal

    places and  a maximum exponent  of 9999 (somewhat  larger range

    than normal BASIC and most scientific calculators).



         All variables  to be used  by the system must  observe the

    above format and  may be initialised to a  starting value using

    the FNCONST routine, e.g.



         number$=FNCONST("1.234567")

         value$=FNCONST("3.101E69")

         old$=FNCONST(STR$(old))



         The  FNCONST routine  will accept  numbers in  any of  the

    above forms.  Note that in  the last example, old$ will contain

    a maximum of  10 significant  figures since  that is  the limit

    imposed by BASIC.



         Having initialised a  variable it is then  possible to use

    any of the commands provided  by the library.  The commands are

    summarised in table  1 and comprise two main  forms.  The first

    type require  only one  string variable to  be passed  to them.

    Examples of these include :



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         neg$=FNNEG(pos$):REM neg=-pos

         sinangle$=FNSIN(angle$):REM sinangle=SIN(angle)

         inta$=FNINT(a$):REM inta=INT(a)



         It is  possible to  include constants  that have  not been

    created using FNCONST as long  as the format described above is

    used.  The  following statements will achieve  exactly the same

    result:



         pi$=FNACS(FNNEG(FNCONST("1")))

         pi$=FNACS("-1")



         Note from the above example  that it is perfectly possible

    to nest the routines, ie the result of one routine being passed

    directly  to  another.  There  is  no  limit imposed  upon  the

    complexity of a structure except  the normal 250 character line

    length.



         The second type of  instructions require two variables and

    perform the normal mathematical  processes such as addition and

    multiplication  and other  more complicated  functions such  as

    calculating polar angles from rectangular coordinates. They are

    used in the following way :



         aplusb$=FNADD(a$,b$):REM aplusb=a+b

         angle$=FNPOL(x$,y$):REM angle=ATN(y/x)





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         Since all the  numbers are handled as  normal strings then

    all  the normal  BASIC  commands may  be  used.  This  includes

    PRINT, LEFT$, RIGHT$ and MID$.



         Two  other  important  facilities   are  provided  by  the

    routines.  These are FNamDP and FNSUIT.  FNamDP allows the user

    to set the  number of decimal places to be  returned (and value

    between 0 and 18) by the routines.  It is used in the following

    way :



         past=FNamDP(14):REM Sets no. of decimal places to 14 and

                             returns with past set to previous

                             value.



         The routine sets  the default number of  decimal places to

    18.  The  second function  FNSUIT is provided  for convenience.

    Since  all the  numbers  are  stored in  a  string  form it  is

    perfectly acceptable  to use  the VAL instruction  to determine

    the  value  of a  string.   However,  because of  the  extended

    accuracy  and  range,  some  numbers  will  be  unsuitable  for

    conversion to BASIC floating point variables and will result in

    a 'Number too  large' error.   To allow you  to determine  if a

    number  is  suitable  for  conversion  the  FNSUIT  command  is

    provided.  It  will return a  TRUE value  if the number  can be

    expressed by a BASIC variable and  FALSE if not.  It is used in

    the following way :



         IF FNSUIT(extnum$) THEN a=VAL(extnum$) ELSE a=0



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         Note the use of a floating point basic variable and not an

    integer one which  would cause rounding to occur  if the number

    has a fraction part.



         When using  the package  it is  best to  use a  mixture of

    extended  precision numbers  and normal  BASIC variables  where

    possible since the calculations with extended precision numbers

    are fairly slow  due to the complex encoding  and decoding that

    occurs with  every command.   It is advised  that they  only be

    used where  strictly necessary  (ie when extended  precision or

    range  is required).   Also,  only use  the  minimum number  of

    decimal  places required  since  extra  decimal places  require

    extra processing and so slow the package unnecessarily.































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    Table 1. Routines provided and their functions.



         Routine name              Function

         ====================================================

         num$=FNCONST("123")      | num$="123"

         num$=FNNEG(num$)         | num$=-num$

         num$=FNABS(num$)         | num$=ABS(num$)

         num$=FNINT(num$)         | num$=INT(num$)

         num$=FNSQR(num$)         | num$=SQR(num$)

         num$=FNLOG(num$)         | num$=LOG(num$)

         num$=FNLN(num$)          | num$=LN(num$)

         num$=FNEXP(num$)         | num$=EXP(num$)

         num$=FNSIN(num$)         | num$=SIN(num$)

         num$=FNCOS(num$)         | num$=COS(num$)

         num$=FNTAN(num$)         | num$=TAN(num$)

         num$=FNASN(num$)         | num$=ASN(num$)

         num$=FNACS(num$)         | num$=ACS(num$)

         num$=FNATN(num$)         | num$=ATN(num$)

         num$=FNADD(a$,b$)        | num$=a$+b$

         num$=FNMUL(a$,b$)        | num$=a$*b$

         num$=FNSUB(a$,b$)        | num$=a$-b$

         num$=FNDIV(a$,b$)        | num$=a$/b$

         num$=FNPOW(a$,b$)        | num$=a$^b$

         num$=FNMOD(a$,b$)        | num$=a$ MOD b$

         num$=FNPOL(a$,b$)        | num$=ATN(b$/a$)

         FNamDP(new)              | sets no. of dec. places

         FNSUIT(num$)             | TRUE if BASIC can express it





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