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Ingy döt Net
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┌──────────────────────────────────────────────────────────────────────────┐
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│ One common method that ensures enough accuracy in REXX is specifying │
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│ more precision (via NUMERIC DIGITS nnn) than is needed, and then │
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│ displaying the number of digits that are desired, or the number(s) │
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│ could be re-normalized using the FORMAT bif. │
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│ │
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│ The technique used (below) is to set the numeric digits ten higher │
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│ than the desired digits, as specified by the SHOWDIGS variable. │
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└──────────────────────────────────────────────────────────────────────────┘
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109
Task/Trigonometric-functions/REXX/trigonometric-functions-2.rexx
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109
Task/Trigonometric-functions/REXX/trigonometric-functions-2.rexx
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/*REXX program demonstrates some common trig functions (30 digits shown)*/
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showdigs=30 /*show only 30 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.'; 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 TAN 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; 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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/*──────────────────────────────────subroutines─────────────────────────*/
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Asin: procedure; arg x; if x<-1 | x>1 then call AsinErr; s=x*x
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if abs(x)>=.7 then return sign(x)*Acos(sqrt(1-s)); z=x; o=x; p=z
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do j=2 by 2; o=o*s*(j-1)/j; z=z+o/(j+1); if z=p then leave; p=z; end
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return z
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Atan: procedure; arg x; if abs(x)=1 then return pi()/4*sign(x)
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return Asin(x/sqrt(1+x**2))
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cos: procedure; arg x; x=r2r(x); a=abs(x); numeric fuzz min(9,digits()-9)
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if a=pi() then return -1; if a=pi()/2 | a=2*pi() then return 0
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if a=pi()/3 then return .5; if a=2*pi()/3 then return -.5
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return .sinCos(1,1,-1)
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sin: procedure; arg x; x=r2r(x); numeric fuzz min(5,digits()-3)
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if abs(x)=pi() then return 0; return .sinCos(x,x,1)
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.sinCos: parse arg z 1 p,_,i; x=x*x
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do k=2 by 2; _=-_*x/(k*(k+i));z=z+_;if z=p then leave;p=z;end; return z
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sqrt: procedure; parse arg x; if x=0 then return 0; d=digits();numeric digits 11
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g=.sqrtGuess(); do j=0 while p>9; m.j=p; p=p%2+1; end
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do k=j+5 to 0 by -1; if m.k>11 then numeric digits m.k; g=.5*(g+x/g); end
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numeric digits d; return g/1
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.sqrtGuess: if x<0 then call sqrtErr; numeric form; m.=11; p=d+d%4+2
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parse value format(x,2,1,,0) 'E0' with g 'E' _ .; return g*.5'E'_%2
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e: return,
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2.7182818284590452353602874713526624977572470936999595749669676277240766303535
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/*Note: the "real: 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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/*If more than 1 million digits are required, be patient. */
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exp: procedure; 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=z*e()**ix; return z
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pi: return, /*a bit of overkill, but hey !! */
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3.1415926535897932384626433832795028841971693993751058209749445923078164062862
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/*Note: the real 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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/*If more than 1 million digits are required, be patient. */
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Acos: procedure; arg x; if x<-1|x>1 then call AcosErr; return .5*pi()-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(arg(1)))
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tan: procedure; 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►1 unit circle*/
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d2r: return r2r(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)//(2*pi()) /*normalize radians►1 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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sqrtErr: call tellErr "sqrt(x), X can't be negative, X="||x
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/* ┌───────────────────────────────────────────────────────────────┐
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│ Not included here are: (among others): │
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│ some of the usual higher-math functions normally associated │
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│ with trig functions: POW, GAMMA, LGGAMMA, ERF, ERFC, ROOT, │
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│ LOG (LN), LOG2, LOG10, ATAN2, │
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│ all of the hyperbolic trig functions and their inverses, │
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│ (too many to name here). │
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│ Angle conversions/normalizations: degrees/radians/grads/mils │
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│ [a circle = 2 pi radians, 360 degrees, 400 grads, 6400 mils].│
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│ Some of the other trig functions (hypens added intentially): │
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│ CHORD │
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│ COT (co-tangent) │
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│ CSC (co-secant) │
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│ CVC (co-versed cosine) │
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│ CVS (co-versed sine) │
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│ CXS (co-exsecant) │
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│ HAC (haver-cosine) │
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│ HAV (haver-sine │
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│ SEC (secant) │
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│ VCS (versed cosine or vercosine) │
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│ VSN (versed sine or versine) │
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│ XCS (exsecant) │
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│ COS/SIN/TAN cardinal (damped COS/SIN/TAN function) │
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│ COS/SIN integral │
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│ and all pertinent of the above's inverses (AVSN, ACVS...) │
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└───────────────────────────────────────────────────────────────┘ */
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