Roots of a quadratic function: Difference between revisions

Line 1,750:

Since "unlimited" decimal precision is part of the REXX language, the   '''numeric digits'''   was increased

<br>(from a default of   '''9''')   to   '''200'''   to accommodate a root closer to zero than the other root.

<br>(from a default of   '''9''')   to   '''200'''   to accommodate when a root is closer to zero than the other root.

Note that only ten decimal digits (precision) are shown in the displaying of the output.

Note that only ten decimal digits (precision) are shown in the   ''displaying''   of the output.

This REXX version supports   ''complex numbers''   for the result.

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quadratic: parse arg aa,bb,cc /*obtain the specified three arguments.*/

$=sqrt(bb**2-4*aa*cc); L=length($) /*compute SQRT (which may be complex).*/

rp=1/(aa+aa); c?=right($,1)=='i' /*compute reciprocal of 2*aa; Complex?*/

r=1/(aa+aa); ?=right($,1)=='i' /*compute reciprocal of 2*aa; Complex?*/

if c? then do~~; n=left($,L-1)~~; r1=-bb*rp; r2=r1; r1j=n*rp; r2j=-r1j; end

if ? then do; r1= -bb *r; r2=r1; r1j=left($,L-1)*r; r2j=-r1j; end

else do; r1=(-bb+$)*rp; r2=(-bb-$)*rp; ~~r1j=0;~~ r2j=0; end

else do; r1=(-bb+$)*r; r2=(-bb-$)*r; r1j=0; r2j= 0; end

return

/*────────────────────────────────────────────────────────────────────────────*/

sqrt: procedure; parse arg x; if x=0 then return 0; d=digits()~~; i=~~; m.=9

sqrt: procedure; parse arg x 1 ox; if x=0 then return 0; d=digits(); m.=9

numeric digits 9; numeric form; h=d+6; if ~~x<0 then do;~~ x=-x~~; i='i'; end~~

numeric digits 9; numeric form; h=d+6; x=abs(x)

parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'e'_%2

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.*/</lang>

numeric digits d; return (g/1)left('i',ox<0) /*make complex if OX<0.*/</lang>

'''output'''   when using the input of:   <tt> 1   -10e5   1 </tt>

<pre>

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root2 = 0.000001

</pre>

The following output is when Regina 3.9.1 REXX is used.

'''output'''   when using the input of:   <tt> 1   -10e9   1 </tt>

<pre>

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root1 = 1.000000000E+10

root2 = 1E-10

</pre>

The following output is when R4 REXX is used.

'''output'''   when using the input of:   <tt> 1   -10e9   1 </tt>

<pre>

a = 1

b = -1E+10

c = 1

root1 = 1E+10

root2 = 0.0000000001

</pre>

'''output'''   when using the input of:   <tt> 3   2   1 </tt>