LF: sine calculus

To: list-fargo@lists.ticalc.org
Subject: LF: sine calculus
From: Hmlacage@aol.com
Date: Sun, 29 Jun 1997 08:18:11 -0400 (EDT)
Reply-To: list-fargo@lists.ticalc.org
I am sorry: last  message about "prog stuff" and my sine lib was  a little
confused... I hadn' t thought about my comments being in french...
So: to make myself clear: i wish to calculate a sine using : sine(x)=x -
x^3/3! + x^5/5! - ...
here is the pseudo code i wrote to do this: 

Table Descriptor:

D0: entry parameters to the program
D1: answer of the program
D2: number of digits in the entry and the answer
D3: exit of the "calc" subroutine: intermediate terms
D4: temporary counter
D6: Counter : power of the calculated term
D7: Counter : number of the calculated term

Pseudo code:

* initialisation of all data regs:
  ex: #1500->D0  ( sine(1.500)
  1->D6,D7,A5
  #1000->D2 ( 4 numbers: 10^(4-1) )
  0->all others
* start:
  * 1st term: D0->D1 ( sin(x) = x+... )
  * iter_1:
    * increase D6,D7 : D6+2->D6 and D7+1->D7
    * branch to "calc" ( in param D6 ( power of the term to calculate )
    out param D3 ( term calculated ) )  
    * test if D7 is odd or even ( in fact test on the sign of the term
    added to D1 )
      * odd: substract D3 to D1
      * even: add D3 to D1
    * test if D3=0 ( test on precision )
      * yes: exit
      * no: branch to iter_1
* end

* calc: ( in param : D6 . exit: D3 )
  * initialise intermediate counter: D6->D4
  * D0->D3 ( 1st term of the power )
  * iter_2:
    * decrease D4
    * D3*D0->D3 multipling to calc the power
    * D3/D2->D3 dividing because all numbers are multiplied by 1000.
     So dividing by 1000.
    * branch to iter_2 while D4 <> 1
  * init D4: D6->D4
  * iter_3:
    * D3/D4->D3 ( dividing by all naturals between D6 and 1: D3/D6!->D3 )
    * dec D4
    * branch to iter_3 while D4 <> 1
* end_calc

and here is the prog i wrote to do this: 

prog_code:

   jsr     reclib[init]
   clr.l   D0              
   clr.l   D1              
   clr.l   D2              
   clr.l   D3              
   clr.l   D4              
   clr.l   D5              
   clr.l   D6
   clr.l   D7
   move.w  #1500,D0       
   move.w  #1,D6                          
   move.w  #1,D7          
   move.w  D0,D1          
   move.w  #1000,D2        
   move.w  #0,A4           
   move.w  #1,A5          

iterer1:
   add.w   #1,D7           
   Add.w   #2,D6           
   bsr     calc            
   btst    #0,D7           
   bne     diff           
   add.w   D3,D1          
retour:
   cmp     A5,D3           
   bge     fin             
   bra     iterer1         
   rts

calc:
   move.w  #0,D4          
   move.w  D0,D3          
   move.w  D6,D4
\iterer2
   sub.w   #1,D4          
   mulu.l  D0,D3          
   divu.l  D2,D3        
   cmp     D4,A4        
   bne     \iterer2     
   move.w  D6,D4        
\iterer3
   divu.l  D4,D3          
   sub.w   #1,D4          
   cmp     D4,A4           
   bne     \iterer3         

diff:
   sub.w   D3,D1          
   bra     retour

fin:
   move.l  D1,D0
   move.l  #0,D1
   move.l  #3,D2
   move.l  #7,D4
   jsr     hexlib[put_hex]
   jsr     flib[idle_loop]
   rts


For those who got that far, the prog i wrote doesn' t work: it writes 2 diff
hex numbers on the screen ( it should write only one ) and none of these is
the awaited answer.... So if someone has ideas... I would be gratefull for
all help...
Something else: i have been looking at torus code: jimmy used a bin file
containing sine table... someone know if he established this file by hand or
if he wrote a prog building it ?

Mathiue, <hm lacage@aol.com>