2010-02-20, 04:39 AM
(This post was last modified: 2020-12-28, 09:54 AM by boriel.
Edit Reason: Fix code to follow the new syntax
)
Sometimes we're willing to lose accuracy for speed. ZX BASIC uses the spectrum's ROM routines for many of its math functions, and as a result of them being general purpose routines that use 40 bit numbers, well, they can be a bit slow sometimes.
See my article on square roots, for a good example.
Here is a routine to produce SIN(angle) - where angle is in degrees. It uses a lookup table to calculate sin values, and it's a very quick and dirty method, in that it only actually knows 32 angles, and those to only 8 bit precision. It does linear interpolation between these known angles, however, so that does improve things somewhat.
I was actually surprised how precise it was - it's good for at least 2 decimal places, probably 3 as a rule of thumb. The average error is 0.002 That's probably good enough for games that need to calculate angles. It's about 4-5 times faster than the SIN(FLOAT) function, and not even written in native assembler.
If you need better accuracy, it would be fairly easy to change the method to use a bigger table - perhaps 2 bytes per entry, even.
Remember to work out COS and TAN can also use this function - COS is SIN(90+x) and TAN is SIN(x)/COS(x). It should be easy to write COSINE and TANGENT functions to do the adjustments and call the SINE function.
(And this one I didn't copy. It's all mine! Bugs and all. And now it's free for anyone to use.)
See my article on square roots, for a good example.
Here is a routine to produce SIN(angle) - where angle is in degrees. It uses a lookup table to calculate sin values, and it's a very quick and dirty method, in that it only actually knows 32 angles, and those to only 8 bit precision. It does linear interpolation between these known angles, however, so that does improve things somewhat.
I was actually surprised how precise it was - it's good for at least 2 decimal places, probably 3 as a rule of thumb. The average error is 0.002 That's probably good enough for games that need to calculate angles. It's about 4-5 times faster than the SIN(FLOAT) function, and not even written in native assembler.
If you need better accuracy, it would be fairly easy to change the method to use a bigger table - perhaps 2 bytes per entry, even.
Remember to work out COS and TAN can also use this function - COS is SIN(90+x) and TAN is SIN(x)/COS(x). It should be easy to write COSINE and TANGENT functions to do the adjustments and call the SINE function.
(And this one I didn't copy. It's all mine! Bugs and all. And now it's free for anyone to use.)
Code:
FUNCTION SINE(num as FIXED) as FIXED
DIM quad as byte
DIM est1,dif as uByte
while num>360
num=num-360
end while
IF num>180 then
quad=-1
num=num-180
ELSE
quad=1
END IF
IF num>90 then num=180-num: end if
num=((num*31)/90)
dif=num : rem Cast to byte loses decimal
num=num-dif : rem so this is just the decimal bit
est1=PEEK (@sinetable+dif)
dif=PEEK (@sinetable+dif+1)-est1 : REM this is just the difference to the next up number.
num=est1+(num*dif): REM base +interpolate to the next value.
return (num/255)*quad
sinetable:
asm
DEFB 000,013,026,038,051,064,076,088
DEFB 100,112,123,134,145,156,166,175
DEFB 184,193,201,209,216,223,229,234
DEFB 239,243,247,250,252,254,255,255
end asm
END FUNCTION
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