Odyssey Magazine #01 05 марта 1997

Программирование

Assembler - How to calculate the sine assemlere.

    How to 
calculate the sine assembly language ? 


 Phantom Lord (C) 1997
 Music by SHOV


 Probably many have noticed that almost all the effects are 
composed of objects changing or moving along a trajectory on 
the sine. Many of course can argue that there are effects that 
change their shape or coordinates does not sine. To which I can 
only reply: "You not right, young man! ". As said

a very good scholar:


         Any functional relationship

         can be expressed in terms of functions

         sine and cosine.


  But we - mathematics and we know that
sin (x) = cos (x-pi / 2), so the phrase can be
transform as follows:


         Any functional relationship

         can be expressed in terms of

         sinus.


          (C) Phantom Lord



  We return to the topic. So we need to have
sine. We define it with the level of BASIC.

 10 let adr = 49152
 20 for n = 0 to 2 * pi step pi/128
 30 poke adr, sin (n) * 127
 40 let adr = adr +1
 50 next n



  As a result, we obtain a table of 256
bytes. Each value is the table
One of the values ​​of sin (n) * 127. We
multiplied sin (n) at 127, to increase
its range to [-1,1] to
[-127.127]. Now if we take the values ​​of
table strictly in order, we will
take successive values ​​of
sin (n) * 127.

 Write a program for modifying the sine
color attributes of the screen.


AGAIN EI

         HALT

         CALL INC_SIN

         CALL SIN

         CALL IZM

         LD A, # 7F

         IN A, (# FE)

         AND 1

         JR NZ, AGAIN

         RET


INC_SIN LD A, 0

         INC A

         LD (INC_SIN +1), A

         RET


SIN LD A, (INC_SIN +1)

         LD L, A

         LD H, # C0

         LD A, (HL)

         RET


IZM LD HL, # 5800

         LD DE, # 5801

         LD BC, 767

         LD (HL), A

         LDIR

         RET



  INC_SIN procedure allows us to run the entire table, since 
all the values ​​of 256, while increasing 255 per unit once we 
get 0, ie element belonging to the set of definitions of our 
function. This condition is called the frequency of the sine 
function. 

 SIN procedure selects from a table sinus
following value, and IZM fills the screen attributes selected 
value. 


      The transition from "pure" sine to

       some advanced features.

 ABS (SIN (X)) - module sinus.



  Of course in mathematics of high school you
probably know that the sine function module is periodic with 
period PI. Let's consider segment of the restriction of SIN (X) 
on poluotrezke [0, PI / 2). It is easy to notice in this case 
the functions are identical. Write a program calculated the 
function ABS (SIN X) based on the reasoning set forth above:


A_1 CALL SIN_INC

         CALL SIN

         JR A_1

SIN_INC LD A, 0

         INC A

         AND 127

         LD (SIN_INC +1), A

         RET


SIN ...


 As you can see after the team we have put INC A AND 127, 
thereby limiting the value of SIN only for positive numbers, ie 
on ABS (SIN (X)). 

 -ABS (SIN (X))


 Obviously, if prodelyvat similar arguments, we obtain a program
similar to the previous one and differs from
it only routine SIN_INC:

SIN_INC LD A, 0

         INC A

         AND 127

         ADD A, 128

         LD (SIN_INC +1), A

         RET

 Now the question may arise:


     And it gives our program?



  This will give your program the realism. Tell me, what nicer 
looking, by bouncing to the laws of physics ball

or mayachuschuyu up-down physical
form?

 You decide.

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