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June 2018 Update

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Ingy döt Net 2018-06-22 20:57:24 +00:00
parent ba8067c3b7
commit 22f33d4004
5278 changed files with 84726 additions and 14379 deletions
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40
Task/Haversine-formula/REXX/haversine-formula.rexx
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@ -5,21 +5,21 @@ say " Los Angles: north 33º 56.4', west 118º 24.0' = 33.94º, -118.4
@using_radius= 'using the mean radius of the earth as ' /*a literal for SAY.*/
radii.=.; radii.1=6372.8; radii.2=6371 /*mean radii of the earth in kilometers*/
say; m=1/0.621371192237 /*M: one statute mile in " */
do radius=1 while radii.radius\==. /*calc. distance using specific radius.*/
do radius=1 while radii.radius\==. /*calc. distance using specific radii. */
d=surfaceDistance( 36.12, -86.67, 33.94, -118.4, radii.radius); say
say center(@using_radius radii.radius ' kilometers', 75, '─')
say ' Distance between: ' format(d/1 ,,2) " kilometers,"
say ' or ' format(d/m ,,2) " statute miles,"
say ' or ' format(d/m*5280/6076.1,,2) " nautical (or air miles)."
end /*radius*/ /*these └───◄ displays 2 decimal digs.*/
end /*radius*/ /*show──┘ 2 dec. digs past dec. point*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
Acos: return .5*pi() - aSin( arg(1) )
d2d: return arg(1) // 360 /*normalize degrees to a unit circle. */
d2r: return r2r(arg(1)*pi() / 180) /*normalize and convert deg ──► radians*/
r2d: return d2d((arg(1)*180 / pi())) /*normalize and convert rad ──► degrees*/
r2r: return arg(1) // (pi()*2) /*normalize radians to a unit circle. */
p: return word(arg(1),1) /*pick the first of two words (numbers)*/
Acos: return pi() * .5 - aSin( arg(1) ) /*calculate the ArcCos of an argument. */
d2d: return arg(1) // 360 /*normalize degrees to a unit circle. */
d2r: return r2r( arg(1) * pi() / 180) /*normalize and convert deg ──► radians*/
r2d: return d2d( (arg(1) * 180 / pi())) /*normalize and convert rad ──► degrees*/
r2r: return arg(1) // (pi() * 2) /*normalize radians to a unit circle. */
p: return word( arg(1), 1) /*pick the first of two words (numbers)*/
pi: pi=3.141592653589793238462643383279502884197169399375105820975; return pi
/*──────────────────────────────────────────────────────────────────────────────────────*/
surfaceDistance: parse arg th1,ph1,th2,ph2,r /*use haversine formula for distance.*/
@ -31,23 +31,23 @@ surfaceDistance: parse arg th1,ph1,th2,ph2,r /*use haversine formula for d
z= sin(th1) - sin(th2)
return Asin( sqrt( x**2 + y**2 + z**2) / 2 ) * r * 2
/*──────────────────────────────────────────────────────────────────────────────────────*/
Asin: procedure; parse arg x 1 z 1 o 1 p; a=abs(x); aa=a*a
if a>=sqrt(2) * .5 then return sign(x) * Acos(sqrt(1-aa))
do j=2 by 2 until p=z; p=z; o=o*aa*(j-1)/j; z=z+o/(j+1); end /*j*/
return z /* [↑] compute until no more noise. */
Asin: procedure; parse arg x 1 z 1 o 1 p; a=abs(x); aa=a * a
if a>=sqrt(2) * .5 then return sign(x) * Acos( sqrt(1 - aa) )
do j=2 by 2 until p=z; p=z; o=o*aa* (j-1) /j; z=z + o/(j+1); end /*j*/
return z /* [↑] compute until no more noise. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
cos: procedure; parse arg x; x=r2r(x); a=abs(x); Hpi=pi*.5
numeric fuzz min(6,digits()-3); if a=pi() then return -1
if a=Hpi | a=Hpi*3 then return 0; if a=pi()/3 then return .5
if a=pi()*2/3 then return -.5; return .sinCos(1,1,-1)
cos: procedure; parse arg x; x=r2r(x); a=abs(x); Hpi=pi * .5
numeric fuzz min(6, digits() - 3) ; if a=pi then return -1
if a=Hpi | a=Hpi*3 then return 0 ; if a=pi/3 then return .5
if a=pi * 2 / 3 then return -.5; return .sinCos(1, 1, -1)
/*──────────────────────────────────────────────────────────────────────────────────────*/
sin: procedure; parse arg x; x=r2r(x); numeric fuzz min(5, digits()-3)
if abs(x)=pi() then return 0; return .sinCos(x,x,1)
sin: procedure; parse arg x; x=r2r(x); numeric fuzz min(5, digits() - 3)
if abs(x)=pi then return 0; return .sinCos(x, x, +1)
/*──────────────────────────────────────────────────────────────────────────────────────*/
.sinCos: parse arg z 1 p,_,i; q=x*x
do k=2 by 2; _=-_*q/(k*(k+i)); z=z+_; if z=p then leave; p=z; end; return z
/*──────────────────────────────────────────────────────────────────────────────────────*/
sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); m.=9; numeric form; h=d+6
numeric digits; parse value format(x,2,1,,0) 'E0' with g "E" _ .; g=g * .5'e'_ % 2
do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/
do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/
do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/
do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/; return g