Home » Archimedes archive » Acorn User » AU 1995-11.adf » !Regulars » Regulars/StarInfo/Radford/ReadMe
Regulars/StarInfo/Radford/ReadMe
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Archimedes archive » Acorn User » AU 1995-11.adf » !Regulars |
| Filename: | Regulars/StarInfo/Radford/ReadMe |
| Read OK: | ✔ |
| File size: | 0F6B bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
Detailed on this disk are several Assembler Libraries that will add, multiply and divide any number to an unlimited degree of accuracy dependent only upon memory constraints. Currently these limits are set to numbers of 400 digits in length, but these may be altered to suit numbers of any length.
The three files "ASS_ADD", "ASS_DIV", "ASS_MUL" are demonstration files of the routines and will add, divide and multiply any integers up to 400 digits in length. To run these simply double click on the file and type in the numbers you wish the routine to operate on.
The three libraries are unified into one general library called "Calc_lib", thus all of these routines can be used from any basic program without any understanding of how these routines work. This library is used as follows:-
i.) First you must make a call to assemble the code this is done with the following command
PROCassemble_calculator
ii.) Next you must specify the operand to be used by the respective routine, this is done as follows:-
operand1$=" first number "
operand2$=" second number "
operand1?0=0
operand2?0=0
FOR A=1 TO LEN(operand1$)
operand1?(A)=VAL(MID$(operand1$,A,1))
NEXT
operand1?(A)=10
FOR A=1 TO LEN(operand2$)
operand2?(A)=VAL(MID$(operand2$,A,1))
NEXT
operand2?(A)=10
Each routine takes its input as a series of bytes contained in operand1 and operand2, the first byte of which must be a 0. values of 1-9 correspeond to the actual digits one to nine, and a value of ten corresponds to the terminating byte in each of the operands, e.g. to specify operand 1 as 21 you could use the following :-
operand1?0=0 \ leading 0
operand1?1=2
operand1?2=1
operand1?3=10 \ terminating byte
iii.)
finally you must call the routine:-
USE EITHER : CALL begin_addition
: CALL begin_division
: CALL begin_multiplication
the result is returned in the variable 'result' and is terminated by a value of 10, it could be accessed as follows:-
A=0
REPEAT
PRINT STR$((result?A));
A+=1
UNTIL result?(A+1)=10
IF both operands 1 and 2 and the result were passed as simple strings then calculations would be restricted to a maximum accuracy of 256 digits, since this is the maximum length for a string under RISC OS, this is why the above convention for passing the operands is used.
Floating point addition, division, and multiplication can be achieved by multiplying up the first operand by a very large number, say 10^100, the result is in effect (10^100 * the answer) and will include 10^100 digits past the decimal point. e.g. to divide 1 by 3 could be done as follows :
make operand 1 = 10^100
make operand 2 = 3
call the division routine
The result will be given as 10^100 * 1/3.
A more complex example of this is given by the program "ASS_ECALC". This program calculates the number e (normally detailed as 2.718281828459) to a specified degree of accuracy. It uses the basis that e can be calculated from the expansion :-
e = { 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + ..... 1/n! }
This program can calculate the factorial of very large numbers - a separate routine that illustrates this is called "fctrial" on the disc.
the final result is given as e * 10^accuracy, where accuracy is the initial accuracy specified.
The accuracy of the result, and the number of terms used to provide the approximation can be altered by changing the following variables at the beginning of the program:-
it%= the number of iterations (initially 100)
acc2% = the accuracy of the result (initially 100)
*********************************************************************************************
** the number 'e' listed to 1990 decimal places in contained in the file 'e' - the program **
** took just under 24 hours to calculate all 2000 terms to nearly 2000 decimal places **
*********************************************************************************************
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00000bd0 2f 32 21 20 2b 20 31 2f 33 21 20 2b 20 31 2f 34 |/2! + 1/3! + 1/4|
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00000d60 72 69 61 62 6c 65 73 20 61 74 20 74 68 65 20 62 |riables at the b|
00000d70 65 67 69 6e 6e 69 6e 67 20 6f 66 20 74 68 65 20 |eginning of the |
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00000db0 6c 6c 79 20 31 30 30 29 0a 61 63 63 32 25 20 3d |lly 100).acc2% =|
00000dc0 20 74 68 65 20 61 63 63 75 72 61 63 79 20 6f 66 | the accuracy of|
00000dd0 20 74 68 65 20 72 65 73 75 6c 74 20 28 69 6e 69 | the result (ini|
00000de0 74 69 61 6c 6c 79 20 31 30 30 29 0a 0a 0a 20 2a |tially 100)... *|
00000df0 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a |****************|
*
00000e40 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 0a 20 2a 2a |************. **|
00000e50 20 74 68 65 20 6e 75 6d 62 65 72 20 27 65 27 20 | the number 'e' |
00000e60 6c 69 73 74 65 64 20 74 6f 20 31 39 39 30 20 64 |listed to 1990 d|
00000e70 65 63 69 6d 61 6c 20 70 6c 61 63 65 73 20 69 6e |ecimal places in|
00000e80 20 63 6f 6e 74 61 69 6e 65 64 20 69 6e 20 74 68 | contained in th|
00000e90 65 20 66 69 6c 65 20 27 65 27 20 2d 20 74 68 65 |e file 'e' - the|
00000ea0 20 70 72 6f 67 72 61 6d 20 2a 2a 0a 20 2a 2a 20 | program **. ** |
00000eb0 74 6f 6f 6b 20 6a 75 73 74 20 75 6e 64 65 72 20 |took just under |
00000ec0 32 34 20 68 6f 75 72 73 20 74 6f 20 63 61 6c 63 |24 hours to calc|
00000ed0 75 6c 61 74 65 20 61 6c 6c 20 32 30 30 30 20 74 |ulate all 2000 t|
00000ee0 65 72 6d 73 20 74 6f 20 6e 65 61 72 6c 79 20 32 |erms to nearly 2|
00000ef0 30 30 30 20 64 65 63 69 6d 61 6c 20 70 6c 61 63 |000 decimal plac|
00000f00 65 73 20 20 20 20 20 20 2a 2a 0a 20 2a 2a 2a 2a |es **. ****|
00000f10 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a |****************|
*
00000f60 2a 2a 2a 2a 2a 2a 2a 2a 2a 0a 0a |*********..|
00000f6b 
.