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Horizontal sundial calculations: Difference between revisions
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added the REXX language.
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HR= 5; HRA= 75.500; HLA=-18.451
HR= 6; HRA= 90.500; HLA= 84.225
</pre>
=={{header|REXX}}==
REXX doesn't have the usual trig functions, nor for that matter, a SQRT (square
root)
<br> function, so these as well as PI were added to this program.
<br><br>No attempt was made to explain the inner workings of these functions.
<lang rexx>
/*REXX program shows hour/sun hour angle/dial hour line angle, 6am->6pm.*/
numeric digits 60 /*better overkill then underkill. */
parse arg lat lng mer . /*get the arguments (if any). */
/*If none specified, then use the */
/*default of Jules Verne's Lincoln*/
/*Island, aka Ernest Legouve Reef.*/
if lat=='' | lat==',' then lat=-4.95 /*No argument? Then use default.*/
if lng=='' | lng==',' then lng=-150.5 /*No argument? Then use default.*/
if mer=='' | mer==',' then mer=-150 /*No argument? Then use default.*/
L=max(length(lat),length(lng),length(mer))
say; say ' latitude:' right(lat,L)
say ' longitude:' right(lng,L)
say ' legal meridian:' right(mer,L); say; say
sineLat=sin(d2r(lat))
w1=max(length('hour'),length('midnight'))+2
w2=max(length('sun hour') ,length('angle'))+2
w3=max(length('dial hour'),length('line angle'))+2
indent=left('',25) /*make presentation prettier. */
say indent center(' ',w1) center('sun hour',w2) center('dial hour' ,w3)
say indent center('hour',w1) center('angle' ,w2) center('line angle',w3)
call sep /*add seperator line for eyeballs*/
do h=-6 to 6 /*Okey dokey then, let's get busy*/
select
when abs(h)==12 then hc='midnight' /*above artic circle ? */
when h<0 then hc=-h 'am' /*convert hour for human beans. */
when h==0 then hc='noon' /* ... easy to understand now. */
when h>0 then hc=h 'pm' /* ... even meaningfull. */
end
hra=15*h-lng+mer
hla=r2d(Atan(sineLat*tan(d2r(hra))))
say indent center(hc,w1) right(format(hra,,1),w2) right(format(hla,,1),w3)
end
call sep
exit
/*looking at subroutines is like looking at saugages being made. Don't.*/
/*─────────────────────────────────────subroutines──────────────────────*/
sep: say indent copies('=',w1) copies('=',w2) copies('=',w3); return
pi: return, /*a bit of overkill, but hey !! */
3.1415926535897932384626433832795028841971693993751058209749445923078164062862
d2d: return arg(1)//360 /*normalize degrees►1 unit circle*/
d2r: return r2r(arg(1)*pi()/180) /*convert degrees ──► radians. */
r2d: return d2d((arg(1)*180/pi())) /*convert radians ──► degrees. */
r2r: return arg(1)//(2*pi()) /*normalize radians►1 unit circle*/
tan: procedure; arg x; _=cos(x); if _=0 then call tanErr; return sin(x)/_
tanErr: call tellErr 'tan('||x") causes division by zero, X="||x
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; 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=2*pi() then return 0;
if a=pi()/3 then return .5; if a=2*pi()/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
Asin: procedure; arg x; if x<-1 | x>1 then call AsinErr; s=x*x;
if abs(x)>=.7 then return sign(x)*Acos(sqrt(1-s)); z=x; o=x; p=z;
do j=2 by 2; o=o*s*(j-1)/j; z=z+o/(j+1); if z=p then leave; p=z; end;
return z
sqrt: procedure; parse arg x; if x=0 then return 0;d=digits();numeric digits 11;
g=sqrtGuess(); do j=0 while p>9; m.j=p; p=p%2+1; end;
do k=j+5 to 0 by -1; if m.k>11 then numeric digits m.k; g=.5*(g+x/g); end;
numeric digits d; return g/1
sqrtGuess: if x<0 then call sqrtErr; numeric form scientific; m.=11; p=d+d%4+2;
parse value format(x,2,1,,0) 'E0' with g 'E' _ .; return g*.5'E'_%2
</lang>
Output:
<pre style="height:30ex;overflow:scroll">
latitude: -4.95
longitude: -150.5
legal meridian: -150
sun hour dial hour
hour angle line angle
========== ========== ============
6 am -89.5 84.2
5 am -74.5 17.3
4 am -59.5 8.3
3 am -44.5 4.8
2 am -29.5 2.8
1 am -14.5 1.3
noon 0.5 0.0
1 pm 15.5 -1.4
2 pm 30.5 -2.9
3 pm 45.5 -5.0
4 pm 60.5 -8.7
5 pm 75.5 -18.5
6 pm 90.5 84.2
========== ========== ============
</pre>
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