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Roots of a quadratic function: Difference between revisions
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m (→version 1: used nine digits precision for the output, simplified the code, use a template for the output sections, added/changed whitespace and comments.) |
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This REXX version supports ''complex numbers'' for the result.
<lang rexx>/*REXX program finds the roots (which may be complex) of a quadratic function. */
parse arg a b c . /*obtain the specified arguments: A B C*/
call quad a,b,c /*solve quadratic function via the sub.*/
r1= r1/1; r2= r2/1; a= a/1; b= b/1; c= c/1 /*normalize numbers to a new precision.*/
if r1j\=0 then r1=r1||left('+',r1j>0)(r1j/1)"i" /*Imaginary part? Handle complex number*/
if r2j\=0 then r2=r2||left('+',r2j>0)(r2j/1)"i" /* " " " " " */
say ' a =' a /*display the normalized value of A. */
say ' b =' b /* " " " " " B. */
say ' c =' c /* " " " " " C. */
say; say 'root1 =' r1 /* " " " " 1st root*/
say 'root2 =' r2 /* " " " " 2nd root*/
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
quad: parse arg aa,bb,cc; numeric digits 200 /*obtain 3 args; use enough dec. digits*/
$= sqrt(bb**2-4*aa*cc); L= length($) /*compute SQRT (which may be complex).*/
r= 1 /(aa+aa); ?= right($, 1)=='i' /*compute reciprocal of 2*aa; Complex?*/
if ? then do; r1= -bb *r; r2=r1; r1j= left($,L-1)*r; r2j=-r1j; end
else do; r1=(-bb+$)*r; r2=(-bb-$)*r; r1j= 0; r2j= 0; end
return
/*──────────────────────────────────────────────────────────────────────────────────────*/
sqrt: procedure; parse arg x 1 ox; if x=0 then return 0; d= digits(); m.= 9; numeric form
numeric digits 9; h= d+6; x=abs(x); 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)left('i', ox<0) /*make complex if OX<0. */</lang>
{{out|output|text= when using the input of: <tt> 1 -10e5 1 </tt>}}
<pre>
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