* * SinCos.asm (of PCQ Pascal) * * These routines replace earlier attempts at the sine and * cosine functions. They are based on the series * representations of the functions, so they're much more * accurate for most of the curve. * * Martin Combs sent me a Pascal version of the implementation * used here. I had been looking at various series for exp() * and ln(), but I didn't like the algorithms I was coming up * with for sine and cosine. Thus I appreciate Martin's * contribution. * * Martin's original Pascal functions duplicated by the assembly * below are: * * FUNCTION sine(x:REAL):REAL; * * FUNCTION GetVal : REAL; * CONST rfac2 = 0.5; {rfac stands for reciprocal of factorial} * rfac3 = 0.1666667; * rfac4 = 0.0416667; * rfac5 = 0.0083333; * sincosfourthpi = 0.7071068; {sine or cosine of pi/4} * VAR x2 : REAL; * {This variation gives four significant figure accuracy} * BEGIN * IF x>fourthpi THEN BEGIN { if x in second octant } * x:=x-fourthpi; { reduce x to first octant } * x2:=sqr(x); * x2:=x2*(rfac4*x2-rfac2)+1.0; {calculates cosine in first octant} * { above is cos(x)=1-(x^2)/2!+(x^4)/4! } * GETVAL:=sincosfourthpi*(sine(x)+x2) { note the recursion } * { Note: sin(x)=sin((x-pi/4)+pi/4)=sin(x-pi/4)cos(pi/4)+cos(x-pi/4)sin(pi/4)} * { =.7071068(sin(x-pi/4)+cos(x-pi/4)) } * END ELSE * x2:=sqr(x); * GetVal:=x*(x2*(rfac5*x2-rfac3)+1.0) {calculates sine in first octant} * {above is sin(x)=x-(x^3)/3!+(x^5)/5! } * END; * * {This variation gives two significant figure accuracy, but faster} * { BEGIN * IF x>fourthpi THEN BEGIN * x:=x-fourthpi; * x2:=sqr(x); * GetVal:=sincosfourthpi*(sine(x)+1.0-rfac2*x2) } * {cosine portion of above is 1-(x^2)/2! } * { END ELSE * x2:=sqr(x); * GetVal:=x*(1.0-rfac3*x2) * END; } * * * BEGIN * IF (x>twopi) OR (x<0.0) THEN { faster than always doing it } * x:= x-Floor(x/twopi)*twopi; * IF x