YAPC::EU 2018 Glasgow Update!
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REBOL [
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Title: "Trigonometric Functions"
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Author: oofoe
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Date: 2009-12-07
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URL: http://rosettacode.org/wiki/Trigonometric_Functions
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]
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/*REXX program demonstrates some common trig functions (30 decimal digits are shown).*/
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showdigs= 25 /*show only 25 digits of number. */
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numeric digits showdigs + 10 /*DIGITS default is 9, but use */
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/*extra digs to prevent rounding.*/
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say 'Using' showdigs 'decimal digits precision.' /*show # decimal digs being used.*/
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say
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do j=-180 to +180 by 15 /*let's just do a half─Monty. */
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stuff = right(j, 4) 'degrees, rads=' show( d2r(j) ) ,
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' sin=' show( sinD(j) ) ,
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' cos=' show( cosD(J) )
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/*don't let TANGENT go postal. */
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if abs(j)\==90 then stuff=stuff ' tan=' show( tanD(j) )
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say stuff
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end /*j*/
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say
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do k=-1 to +1 by 1/2 /*keep the Arc─functions happy. */
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say right(k, 4) 'radians, degs=' show( r2d(k) ) ,
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' Acos=' show( Acos(k) ) ,
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' Asin=' show( Asin(k) ) ,
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' Atan=' show( Atan(k) )
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end /*k*/
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exit /*stick a fork in it, we're done.*/
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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Asin: procedure; parse arg x 1 z 1 o 1 p; a=abs(x); aa=a*a
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if a>1 then call AsinErr x /*X argument is out of range. */
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if a >= sqrt(2) * .5 then return sign(x) * acos( sqrt(1 - aa), '-ASIN')
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do j=2 by 2 until p=z; p=z; o= o * aa * (j-1) / j; z= z +o / (j+1); end
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return z /* [↑] compute until no noise. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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Acos: procedure; parse arg x; if x<-1 | x>1 then call AcosErr; return pi()*.5 - Asin(x)
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AcosD: return r2d( Acos( arg(1) ) )
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AsinD: return r2d( Asin( arg(1) ) )
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cosD: return cos( d2r( arg(1) ) )
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sinD: return sin( d2r( d2d( arg(1) ) ) )
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tan: procedure; parse arg x; _= cos(x); if _=0 then call tanErr; return sin(x) / _
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tanD: return tan( d2r( arg(1) ) )
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d2d: return arg(1) // 360 /*normalize degrees ──► a unit circle*/
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d2r: return r2r( d2d( arg(1) )*pi() / 180) /*convert degrees ──► radians. */
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r2d: return d2d( ( arg(1) * 180 / pi() ) ) /*convert radians ──► degrees. */
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r2r: return arg(1) // (pi() *2) /*normalize radians ──► a unit circle*/
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show: return left( left('', arg(1) >= 0)format( arg(1), , showdigs) / 1, showdigs)
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tellErr: say; say '*** error! ***'; say; say arg(1); say; exit 13
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tanErr: call tellErr 'tan(' || x") causes division by zero, X=" || x
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AsinErr: call tellErr 'Asin(x), X must be in the range of -1 ──► +1, X=' || x
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AcosErr: call tellErr 'Acos(x), X must be in the range of -1 ──► +1, X=' || x
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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Atan: procedure; parse arg x; if abs(x)=1 then return pi() * .25 * sign(x)
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return Asin(x / sqrt(1 + x*x) )
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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cos: procedure; parse arg x; x= r2r(x); a=abs(x); hpi= pi * .5
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numeric fuzz min(6, digits() - 3); if a=pi() then return -1
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if a=hpi | a=hpi*3 then return 0; if a=pi() / 3 then return .5
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if a=pi() * 2 / 3 then return -.5; return .sinCos(1, -1)
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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sin: procedure; parse arg x; x=r2r(x); numeric fuzz min(5, max(1, digits() -3))
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if x=pi*.5 then return 1; if x==pi * 1.5 then return -1
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if abs(x)=pi | x=0 then return 0; return .sinCos(x, 1)
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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.sinCos: parse arg z 1 _,i; q= x*x
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do k=2 by 2 until p=z; p= z; _= - _ * q / (k * (k+i) ); z= z+_; end
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return z
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); i=; m.=9; h= d+6
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numeric digits; numeric form; if x<0 then do; x= -x; i= 'i'; end
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parse value format(x, 2, 1, , 0) 'E0' with g 'E' _ .; g= g *.5'e'_ % 2
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do j=0 while h>9; m.j=h; h= h % 2 + 1; end /*j*/
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do k=j+5 to 0 by -1; numeric digits m.k; g= (g+x/g) * .5; end /*k*/
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numeric digits d; return (g/1)i /*make complex if X < 0.*/
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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e: e = 2.7182818284590452353602874713526624977572470936999595749669676277240766303535
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return e /*Note: the actual E subroutine returns E's accuracy that */
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/*matches the current NUMERIC DIGITS, up to 1 million digits.*/
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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exp: procedure; parse arg x; ix=x%1; if abs(x-ix)>.5 then ix= ix + sign(x); x=x - ix
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z=1; _=1; w=z; do j=1; _= _*x/j; z= (z+_) / 1; if z==w then leave; w=z; end
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if z\==0 then z= e()**ix * z; return z
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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pi: pi= 3.1415926535897932384626433832795028841971693993751058209749445923078164062862
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return pi /*Note: the actual PI subroutine returns PI's accuracy that */
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/*matches the current NUMERIC DIGITS, up to 1 million digits.*/
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/*John Machin's formula is used for calculating more digits. */
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