new QSIN (QQSIN)

[Quentin]

like always: It depends on ....

QSIN is working faster as long as the values for the angle value are small. But often, I don't care about the value of the angle, e.g. increment per 1 at each loop for an endless rotation of a sprite. For large values for angle the native SIN funtion from GLBasic is faster.

Example:

Code: GLBasic [Select]

...
time3 = GETTIMERALL()
        FOR i = 0 TO 200000
                z=SIN(i)
        NEXT
diff3 = GETTIMERALL() - time3

counter =0
time4 = GETTIMERALL()
        FOR i = 0 TO 200000
                za= QSIN (i)
        NEXT
diff4 = GETTIMERALL() - time4

counter =0
time5 = GETTIMERALL()
        FOR i = 0 TO 200000
                zs= QSIN_OLD (i)
        NEXT
diff5 = GETTIMERALL() - time5
...

the bigger the values for angle, the more fast the native GLBasic SIN function is. You'll see the same effect with the precalculated SIN values (see lookup sample from Ocean)

Btw: could be interesting to look how math functions could work:

http://stackoverflow.com/questions/345085/how-do-trigonometric-functions-work/345117#345117

[Qedo]

@ Quentin
the new QQSIN for high (and low) angle.
Ciao


[attachment deleted by admin]

[kanonet]

I tried to optimise QSIN/QQSIN and found this to be the fastest on any angle (at least on my machine):

Code: GLBasic [Select]

FUNCTION QQSIN: x
        IF x > 360
                DEC x, INTEGER( x / 360 ) * 360
        ELSEIF  x < 0
                INC x, INTEGER( 1 - x / 360 ) * 360
        ENDIF

        IF x < 180
                x = ( 0.02222144652331750907567718514381 - 0.00012346049003081125437778164739108 * x )* x
                RETURN ( 0.775 + 0.225 *x ) * x
        ENDIF
        x = 180 - x
        x = ( 0.02222144652331750907567718514381 + 0.00012346049003081125437778164739108 * x ) * x
        RETURN ( 0.775 - 0.225 * x ) * x
ENDFUNCTION

[Qedo]

Kanonet
You're right.
Your code is faster on average by 7%
well done
ciao

[Qedo]

sorry Ocean, but I don't understand.
The angles outside 0-360 degrees are redused at the first quadrant but not converted in integer.
Can you give a practical example?

[kanonet]

Not true ocean, i think  you didnt understand the calculation.

But very interesting:

i put some DEBUGs in the code:

Code: GLBasic [Select]

FUNCTION QQSIN: x
DEBUG "start x: "+x
        IF x > 360
                DEC x, INTEGER( x / 360 ) * 360
        ELSEIF  x < 0
                INC x, INTEGER( 1 - x / 360 ) * 360
        ENDIF
DEBUG " calculated x: "+x

        IF x < 180
                x = ( 0.02222144652331750907567718514381 - 0.00012346049003081125437778164739108 * x )* x
DEBUG " sin(x): "+(( 0.775 + 0.225 * x ) * x)+CHR$(10)
                RETURN ( 0.775 + 0.225 *x ) * x
        ENDIF
        x = 180 - x
        x = ( 0.02222144652331750907567718514381 + 0.00012346049003081125437778164739108 * x ) * x
DEBUG " sin(x): "+(( 0.775 - 0.225 * x ) * x)+CHR$(10)
        RETURN ( 0.775 - 0.225 * x ) * x
ENDFUNCTION

if i do:

Code: GLBasic [Select]

QQSIN(60.3)
QQSIN(60.3+360)
QQSIN(60.3-360)
QQSIN(60.3+720)
QQSIN(60.3-720)

i get on debugger:

Code: GLBasic [Select]

start x: 60.3 calculated x: 60.3 sin(x): 0.8691949954
start x: 420.3 calculated x: 60.3 sin(x): 0.8691949954
start x: -299.7 calculated x: 60.3 sin(x): 0.8691949954
start x: 780.3 calculated x: 60.3 sin(x): 0.8691949954
start x: -659.7 calculated x: 60.3 sin(x): 0.8691949954

so basically no difference.

But by coding

Code: GLBasic [Select]

DEBUG (QQSIN(60.3)-QQSIN(60.3+360))

i get:

Code: GLBasic [Select]

-1.110223025e-016

so abruptly there s a very, very small difference... but i think its so small, i think it doesnt matter, 'cuz if you need high precision, you take the GLBasic SIN() and not one of the quicker functions.

[Qedo]

in the Kanonet code eliminated the integer cast  (see code) Now >10% faster (on my computer)

Code: GLBasic [Select]

FUNCTION QQSIN1: x // Kanonet
LOCAL xx%
xx=x
IF xx >= 360
                DEC x, ( xx / 360 ) * 360  // was DEC x, INTEGER( x / 360 ) * 360
 ELSEIF  x < 0
                 INC x, ( 1 - xx / 360 ) * 360 // was INC x, INTEGER( 1 - x / 360 ) * 360
ENDIF

        IF x < 180
                x = ( 0.02222144652331750907567718514381 - 0.00012346049003081125437778164739108 * x )* x
                RETURN ( 0.775 + 0.225 *x ) * x
        ENDIF
        x = 180 - x
        x = ( 0.02222144652331750907567718514381 + 0.00012346049003081125437778164739108 * x ) * x
        RETURN ( 0.775 - 0.225 * x ) * x
ENDFUNCTION
 

@Ocean
your code is very very fast (40% faster) congratulations.
Ingenious the & bAnd control in: return _cos_tbl_[ (int)(x * __d__) & __c__] ;
the other side of the coin is the increased use of memory of the lookup table.
Ciao

[ampos]

I am still amazed that there is a faster formula than just taking a value from a matrix... 

[Qedo]

The Ocean's code use a lookup table and take a value from a matrix.
It's the fastest.
Ciao

[kanonet]

Qedo, you forgot one float, it should be:

Code: GLBasic [Select]

FUNCTION QQSIN: x       // by Kitty Hello, Qedo, Kanonet
        LOCAL xx%=x
        IF xx > 360
                DEC x, INTEGER( xx / 360 ) * 360
        ELSEIF  xx < 0
                INC x, INTEGER( 1 - xx / 360 ) * 360
        ENDIF

        IF x < 180
                x = ( 0.02222144652331750907567718514381 - 0.00012346049003081125437778164739108 * x )* x
                RETURN ( 0.775 + 0.225 *x ) * x
        ENDIF
        x = 180 - x
        x = ( 0.02222144652331750907567718514381 + 0.00012346049003081125437778164739108 * x ) * x
        RETURN ( 0.775 - 0.225 * x ) * x
ENDFUNCTION

On my machine Oceans Code only need 50%-75% of the time... but if you want to save the additional memory or dont want to use INLINE, i think our code is good too.

[Qedo]

Kanonet, the float var controls the negative angles between -1 and 0.
The  integer xx truncated  to 0.
Also the two INTEGER() cast don't need because the whole operations are with integer variables

I like "// by Kitty Hello, Qedo, Kanonet" 

ciao

Code: GLBasic [Select]

Qedo, you forgot one float, it should be:
Code: [Select]

FUNCTION QQSIN: x       // by Kitty Hello, Qedo, Kanonet
        LOCAL xx%=x
        IF xx > 360
                DEC x, INTEGER( xx / 360 ) * 360
        ELSEIF  xx < 0
                INC x, INTEGER( 1 - xx / 360 ) * 360
        ENDIF

[kanonet]

@Ocean:
thanks for your explanation on platform compatibility, good to know, that it will work on every one. Btw. can users of the free version use INLINE?
I wait for your research on memory consumption, so we get more information for decisions.

@Qedo:
i dont think, that that truncating -0.5 to 0 is a problem, we have still 'good' precision. But what do you mean with "Also the two INTEGER() cast don't need because the whole operations are with integer variables"? We need INTEGER() because its part of a modulo operation. Do you want to change something on that code, or is the actual version in my last post?

[Qedo]

Kanonet,
for the negative angles you are right.

for the uselessness of the INTEGER() try this code:
the results are the same
ciao

x=759.1
LOCAL xx%
xx=x
DEBUG ( xx / 360 ) * 360 + CHR$(10)

x=759.1
xx=x
DEBUG INTEGER( xx / 360 ) * 360 + CHR$(10)
END

the code should be:

FUNCTION QQSIN: x   // by Kitty Hello, Qedo, Kanonet
   LOCAL xx%=x
   IF xx > 360
      DEC x, ( xx / 360 ) * 360
   ELSEIF  xx < 0
      INC x, ( 1 - xx / 360 ) * 360
   ENDIF

   IF x < 180
      x = ( 0.02222144652331750907567718514381 - 0.00012346049003081125437778164739108 * x )* x
      RETURN ( 0.775 + 0.225 *x ) * x
   ENDIF
   x = 180 - x
   x = ( 0.02222144652331750907567718514381 + 0.00012346049003081125437778164739108 * x ) * x
   RETURN ( 0.775 - 0.225 * x ) * x
ENDFUNCTION

[kanonet]

Oh you're right. It don't speed it up, but it looks nicer.^^
Btw on my machine QSIN is faster than tSIN for angles 0 to 360 with a stepping of 0.1. But in any other case tSIN is faster.

[kanonet]

interesting and a bit odd, considering what few instructions are involved to retrieve a tSIN from the lookup table.  What machine & OS are you using?

Sorry, forgot to answer you: Im running the machine, that you find in my signature, with Win7 Pro x64.