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2016 Update

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Tina Müller 2016-12-05 22:15:40 +01:00
parent 948b86eafa
commit dcf5d15da3
7965 changed files with 139854 additions and 31002 deletions
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63
Task/Averages-Mean-angle/REXX/averages-mean-angle.rexx
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@ -1,57 +1,54 @@
/*REXX program computes the mean angle (the angles expressed in degrees). */
numeric digits 50 /*use 50 decimal digits of precision,*/
showDig=10 /* but only display ten decimal digits.*/
# = 350 10 ; say showit(#, meanAngleD(#) )
# = 90 180 270 360 ; say showit(#, meanAngleD(#) )
# = 10 20 30 ; say showit(#, meanAngleD(#) )
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────subroutines──────────────────────────────────────────────*/
/*REXX program computes the mean angle for a group of angles (expressed in degrees). */
call pi /*define the value of pi to some accuracy.*/
numeric digits length(pi) - 1; showDig=10 /*use PI width decimal digits of precision,*/
/* but only display 10 decimal digits. */
#=350 10 ; say show(#, meanAngleD(#) )
#=90 180 270 360 ; say show(#, meanAngleD(#) )
#=10 20 30 ; say show(#, meanAngleD(#) )
exit /*stick a fork in it, we're all done with it*/
/*───────────────────────────────────────────────────────────────────────────────────────────*/
.sinCos: arg z,_,i; x=x*x; do k=2 by 2 until p=z; p=z; _=-_*x/(k*(k+i)); z=z+_; end; return z
$fuzz: return min(arg(1), max(1, digits() - arg(2) ) )
acos: procedure; parse arg x; return pi() * .5 - asin(x)
atan: parse arg x; if abs(x)=1 then return pi()*.25 * sign(x); return asin(x/sqrt(1 + x*x))
Acos: procedure; parse arg x; return pi() * .5 - Asin(x)
Atan: parse arg x; if abs(x)=1 then return pi()*.25 * sign(x); return Asin(x/sqrt(1 + x*x))
d2d: return arg(1) // 360
d2r: return r2r(d2d(arg(1)) / 180 * pi() )
r2d: return d2d((r2r(arg(1)) / pi()) * 180)
r2r: return arg(1) // (pi() * 2)
r2r: return arg(1) // (pi() * 2)
p: return word(arg(1), 1)
pi: pi=3.1415926535897932384626433832795028841971693993751058209749445923078164062862;return pi
asin: procedure; parse arg x 1 z 1 o 1 p; xx=x*x
if xx>=.5 then return sign(x) * acos(sqrt(1-xx))
do j=2 by 2 until p=z; p=z; o=o*xx*(j-1)/j; z=z+o/(j+1); end
return z /* [↑] compute until no more noise. */
Asin: procedure; parse arg x 1 z 1 o 1 p; xx=x*x
if xx>=.5 then return sign(x) * Acos(sqrt(1-xx))
do j=2 by 2 until p=z; p=z; o=o*xx*(j-1)/j; z=z+o/(j+1); end /*j*/
return z /* [↑] compute until no more noise.*/
atan2: procedure; parse arg y,x; call pi; s=sign(y)
Atan2: procedure; parse arg y,x; call pi; s=sign(y)
select
when x=0 then z=s * pi * .5
when x<0 then if y=0 then z=pi; else z=s*(pi-abs(atan(y/x)))
otherwise z=s * atan(y/x)
when x<0 then if y=0 then z=pi; else z=s * (pi - abs( Atan(y/x) ) )
otherwise z=s * Atan(y/x)
end /*select*/; return z
cos: procedure; parse arg x; x=r2r(x); numeric fuzz $fuzz(6, 3)
a=abs(x); if a=0 then return 1; if a=pi then return -1
if a=pi*.5 | a=pi*1.5 then return 0; if a=pi/3 then return .5
if a=pi*2/3 then return -.5; return .sinCos(1, 1, -1)
if a=pi*2/3 then return -.5; return .sinCos(1, 1, -1)
meanAngleD: procedure; parse arg x; numeric digits digits()+digits()%4
_sin=0; _cos=0; n=words(x); do j=1 for n; !=d2r(word(x,j))
_sin=_sin + sin(!)
_cos=_cos + cos(!)
end /*j*/
return r2d(atan2(_sin/n, _cos/n))
n=words(x); _sin=0; _cos=0
do j=1 for n; !=d2r(word(x, j)); _sin=_sin+sin(!); _cos=_cos+cos(!); end /*j*/
return r2d(Atan2(_sin/n, _cos/n))
showit: procedure expose showDig; numeric digits showDig; parse arg a,mA
return left('angles='a,30) 'mean angle=' format(mA,,showDig,0)/1
show: parse arg a,mA; _=format(ma, , showDig, 0) / 1
return left('angles='a, 30) "mean angle=" right(_, max(4, length(_)))
sin: procedure; parse arg x; x=r2r(x); numeric fuzz $fuzz(5, 3)
if x=pi*.5 then return 1; if x==pi*1.5 then return -1
if abs(x)=pi | x=0 then return 0; return .sinCos(x, x, +1)
sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); i=; m.=9
numeric digits 9; numeric form; h=d+6; if x<0 then do; x=-x; i='i'; end
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*/
numeric digits d; return (g/1)i /*make complex if X < 0.*/
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*/
return g