This function implements fast Fixed point sin, cos and tan functions. The ones that uses Float type (calling the Sinclair ROM) are much slower as FP Calculations are expensive. This variant is less precise but more suitable for games, for example.
fSin is the basis for the alternatives, since COS(x) can be calculated from SIN(x) and TAN(x) as SIN(x) / COS(x).
The functions should be accurate to about 0.25%, and significantly faster. If you need a lot of trig in your code, and it doesn't need to be pinpoint accuracy, these are good alternatives. Note that they more or less acknowledge they are less accurate by returning values of type Fixed instead of type Float. It should be fine for the actual accuracy returned, and Fixed numbers process faster and smaller than Float ones.
FUNCTION fSin(num as FIXED) as FIXED
DIM quad as byte
DIM est1,dif as uByte
'This change made now that MOD works with FIXED types.
'This is much faster than the repeated subtraction method for large angles (much > 360)
'while having some tiny rounding errors that should not significantly affect our results.
'Note that the result may be positive or negative still, and for SIN(360) might come out
'fractionally above 360 (which would cause issued) so the below code still is required.
IF num >= 360 THEN
num = num MOD 360
ELSEIF num < 0 THEN
num = 360 - ABS(num) MOD 360
END IF
IF num > 180 then
quad = -1
num = num - 180
ELSE
quad = 1
END IF
IF num > 90 THEN num = 180 - num
num = num / 2
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 000,009,018,027,035,044,053,062
DEFB 070,079,087,096,104,112,120,127
DEFB 135,143,150,157,164,171,177,183
DEFB 190,195,201,206,211,216,221,225
DEFB 229,233,236,240,243,245,247,249
DEFB 251,253,254,254,255,255
End Asm
END FUNCTION
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