Horizontal sundial calculations: Difference between revisions

Content added Content deleted
m (→‎{{header|REXX}}: changed extra digits and optimized the sqrt function, added a comment.)
m (→‎{{header|REXX}}: added more FUZZ digits to COS subroutine.)
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tellErr: say; say '*** error! ***'; say; say arg(1); say; exit 13
AsinErr: call tellErr 'Asin(x), X must be in the range of -1 ──► +1, X=' ||x
sqrtErr: call tellErr "sqrt(x), X can't be negative, X=" || x
AcosErr: call tellErr 'Acos(x), X must be in the range of -1 ──► +1, X=' ||x
Acos: procedure; arg x; if x<-1|x>1 then call AcosErr; return .5*pi()-Asin(x)
 
Atan: procedure; arg x; if abs(x)=1 then return pi()/4*sign(x)
return Asin(x/sqrt(1+x**2))
 
sin: procedure; arg x; x=r2r(x); numeric fuzz min(5,digits()-3)
if abs(x)=pi() then return 0; return .sinCos(x,x,1)
 
cos: procedure; parse arg x; x=r2r(x); a=abs(x); numeric fuzz min(9,digits()-9) hpi=pi*.5▼
if a=pinumeric fuzz min(6,digits()/-3); then return .5; if a=pi()*2/3 then return -.51▼
if a=pi()hpi | a=hpi*3 then return -10; if a=pi()/2 | a=pi()*23 then return 0.5▼
if a=pi()*2/3 then return -.5; return .sinCos(1,1,-1)
 
▲cos: procedure; arg x; x=r2r(x); a=abs(x); numeric fuzz min(9,digits()-9)
▲ if a=pi() then return -1; if a=pi()/2 | a=pi()*2 then return 0
▲ if a=pi()/3 then return .5; if a=pi()*2/3 then return -.5
return .sincos(1,1,-1)
.sinCos: parse arg z,_,i; x=x*x; p=z
do k=2 by 2; _=-_*x/(k*(k+i));z=z+_; if z=p then leave; p=z; end; return z
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return z
 
pi: returnpi=, /*a bit of an overkill, but hey !! */
3.1415926535897932384626433832795028841971693993751058209749445923078164062862
return pi /*Note: the real PI subroutine returns PI's accuracy that */
/*matches the current NUMERIC DIGITS, up to 1 million digits.*/
/*John Machin's formula is used for calculating more digits. */
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