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March 2014 update

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Ingy döt Net 2014-04-02 16:56:35 +00:00
parent 09687c4926
commit a25938f123
1846 changed files with 21876 additions and 5203 deletions
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0
Task/Trigonometric-functions/PARI-GP/trigonometric-functions.pari → Task/Trigonometric-functions/PARI-GP/trigonometric-functions-1.pari
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1
Task/Trigonometric-functions/PARI-GP/trigonometric-functions-2.pari Normal file
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@ -0,0 +1 @@
apply(f->f(1), [cos,sin,tan,acos,asin,atan])

47
Task/Trigonometric-functions/REXX/trigonometric-functions-2.rexx
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@ -4,7 +4,7 @@ numeric digits showdigs+10 /*DIGITS default is 9, but use */
/*extra digs to prevent rounding.*/
say 'Using' showdigs 'decimal digits precision.'; say
do j=-180 to +180 by 15 /*let's just do a half-Monty. */
do j=-180 to +180 by 15 /*let's just do a half-Monty. */
stuff = right(j,4) 'degrees, rads='show( d2r(j)),
' sin='show(sinD(j)),
' cos='show(cosD(J))
@ -13,7 +13,7 @@ say 'Using' showdigs 'decimal digits precision.'; say
say stuff
end /*j*/
say; do k=-1 to +1 by 1/2 /*keep the Arc-functions happy. */
say; do k=-1 to +1 by 1/2 /*keep the Arc-functions happy. */
say right(k,4) 'radians, degs='show( r2d(k)),
' Acos='show(Acos(k)),
' Asin='show(Asin(k)),
@ -21,21 +21,21 @@ say; do k=-1 to +1 by 1/2 /*keep the Arc-functions happy. */
end /*k*/
exit /*stick a fork in it, we're done.*/
/*──────────────────────────────────subroutines─────────────────────────*/
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
Asin: procedure; parse arg x 1 z 1 o 1 p; if x<-1 | x>1 then call AsinErr
s=x*x; if abs(x)>=sqrt(2)*.5 then return sign(x)*Acos(sqrt(1-s))
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
Atan: procedure; arg x; if abs(x)=1 then return pi()/4*sign(x)
return Asin(x/sqrt(1+x**2))
Atan: procedure; parse arg x; if abs(x)=1 then return pi()*.25*sign(x)
return Asin(x/sqrt(1+x*x))
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
cos: procedure; parse arg x; x=r2r(x); a=abs(x); numeric fuzz min(9,digits()-9)
if a=pi() then return -1; if a=pi()*.5 | a=pi()*2 then return 0
pi3=pi()/3; if a=pi3 then return .5; if a=2*pi3 then return -.5
return .sinCos(1,1,-1)
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)
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; x=x*x
do k=2 by 2; _=-_*x/(k*(k+i));z=z+_;if z=p then leave;p=z;end; return z
@ -44,41 +44,42 @@ sqrt: procedure; parse arg x; if x=0 then return 0; m.=9; p=digits(); i=
numeric digits 9; if x<0 then do; x=-x; i='i'; end; numeric form; m.0=p
parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'E'_%2; m.1=p
do j=2 while p>9; m.j=p; p=p%2+1; end /*j*/
do k=j+5 to 0 by -1; numeric digits m.k; g=.5*(g+x/g); end /*k*/
do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/
numeric digits m.0; return (g/1)i
e: return,
2.7182818284590452353602874713526624977572470936999595749669676277240766303535
/*Note: the "real: E subroutine returns E's accuracy that */
/*Note: the actual E subroutine returns E's accuracy that */
/*matches the current NUMERIC DIGITS, up to 1 million digits.*/
/*If more than 1 million digits are required, be patient. */
exp: procedure; arg x; ix=x%1; if abs(x-ix)>.5 then ix=ix+sign(x); x=x-ix
exp: procedure; parse arg x; ix=x%1; if abs(x-ix)>.5 then ix=ix+sign(x); x=x-ix
z=1; _=1; w=z; do j=1; _=_*x/j; z=(z+_)/1; if z==w then leave; w=z; end
if z\==0 then z=z*e()**ix; return z
if z\==0 then z=e()**ix*z; return z
pi: return, /*a bit of overkill, but hey !! */
3.1415926535897932384626433832795028841971693993751058209749445923078164062862
/*Note: the real PI subroutine returns PI's accuracy that */
/*Note: the actual 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. */
/*If more than 1 million digits are required, be patient. */
Acos: procedure; arg x; if x<-1|x>1 then call AcosErr; return .5*pi()-Asin(x)
Acos: procedure; parse arg x; if x<-1|x>1 then call AcosErr; return .5*pi()-Asin(x)
AcosD: return r2d(Acos(arg(1)))
AsinD: return r2d(Asin(arg(1)))
cosD: return cos(d2r(arg(1)))
sinD: return sin(d2r(arg(1)))
tan: procedure; arg x; _=cos(x); if _=0 then call tanErr; return sin(x)/_
sinD: return sin(d2r(d2d(arg(1))))
tan: procedure; parse arg x; _=cos(x); if _=0 then call tanErr; return sin(x)/_
tanD: return tan(d2r(arg(1)))
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*/
d2d: return arg(1)//360 /*normalize degrees►1 unit circle. */
d2r: return r2r(d2d(arg(1))*pi()/180) /*convert degrees ──► radians. */
r2d: return d2d((arg(1)*180/pi())) /*convert radians ──► degrees. */
r2r: return arg(1)//(pi()*2) /*normalize radians ──►a unit circle*/
show: return left(left('',arg(1)>=0)format(arg(1),,showdigs)/1,showdigs)
tellErr: say; say '*** error! ***'; say; say arg(1); say; exit 13
tanErr: call tellErr 'tan('||x") causes division by zero, X="||x
AsinErr: call tellErr 'Asin(x), X must be in the range of -1 ──► +1, X='||x
AcosErr: call tellErr 'Acos(x), X must be in the range of -1 ──► +1, X='||x
sqrtErr: call tellErr "sqrt(x), X can't be negative, X="||x
/* ┌───────────────────────────────────────────────────────────────┐
│ Not included here are (among others): │
│ some of the usual higher-math functions normally associated │