Rosetta Code

Roots of unity: Difference between revisions

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Roots of unity (view source)

Revision as of 19:07, 17 August 2020

77 bytes removed ,  3 years ago
m
→‎{{header|REXX}}: added whitespace, aligned statements, changed some comments, optimized the R2R function.
(add FreeBASIC)
m (→‎{{header|REXX}}: added whitespace, aligned statements, changed some comments, optimized the R2R function.)
Line 1,529:
(See the value of the REXX variable &nbsp; '''frac''', &nbsp; 4<sup>th</sup> line).
<lang rexx>/*REXX program computes the K roots of unity (which usually includes complex roots).*/
numeric digits length( pi() ) - 1 /*use number of decimal digits in pi. */
parse arg n frac . /*get optional arguments from the C.L. */
if n=='' | n=="," then n= 1 /*Not specified? Then use the default.*/
if frac='' | frac=="," then frac= 5 /* " " " " " " */
start= abs(n) start= abs(n) /*assume only one K is wanted. */
if n<0 then start= 1 /*Negative? Then use a range of K's. */
numeric digits length( pi() ) - 1 pi2= pi + pi /*useobtain numberthe value of decimal digits inpi pidoubled. */
pi2= pi + pi do #=start to abs(n) /*obtainshow theunity valueroots of(for a range pior 1 doubledK. */
say right(# 'roots of unity', 40, "─ ") ' (showing' frac "fractional decimal digits)"▼
/*display unity roots for a range, or */
do #=start to abs(n) /* just for one K. */
▲ say right(# 'roots of unity', 40, "─") ' (showing' frac "fractional decimal digits)"
do angle=0 by pi2/# for # /*compute the angle for each root. */
rp= adjustadj( cos(angle) ) /*compute real part via COS function.*/
if left(rp, 1) \== '-' then rp= " "rp /*not negative? Then pad with a blank.*/
ip= adjustadj( sin(angle) ) /*compute imaginary part via SIN funct.*/
if left(ip, 1) \== '-' then ip= "+"ip /*Not negative? Then pad with + char.*/
if ip=0 then say rp /*Only real part? Ignore imaginary part*/
else say left(rp, frac+4)ip'i' /*display the real and imaginary part. */
end /*angle*/
end /*#*/
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
pi: pi=3.141592653589793238462643383279502884197169399375105820974944592307816; return pi
r2r: return arg(1) // ( pi() *+ 2pi ) /*reduce #radians: -2pi──►2pi ─► +2pi radians*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
adjustadj: parse arg x; near0= '1e-' || (digits() -* digits()9 % 10) /*compute a tiny number.*/
if abs(x) < near0 then x= 0 /*if it's near zero, then assume zero.*/
return format(x, , frac) / 1 /*fraction digits past decimal point. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
cos: procedure; parse arg x; x= r2r(x); a= abs(x); numeric fuzz min(9, digits()-9)
if a=pi/3 then return .5; if a=pi/2 | a=pi*2 then return 0
if a=pi then return -1; if a=pi*2/3 then return -.5; z= 1; _= 1; $x= x * x
do k=2 by 2 until p=z; p=z; _= - _ * $x / (k*(k-1)); z= z + _; end; return z
/*──────────────────────────────────────────────────────────────────────────────────────*/
sin: procedure; parse arg x; x= r2r(x); numeric fuzz min(5, digits()-3)
if abs(x)=pi then return 0; z= x; _= x; $x= x * x
do k=2 by 2 until p=z; p=z; _= - _ * $x / (k*(k+1)); z= z + _; end; return z</lang>
{{out|output|text=&nbsp; when using the input of: &nbsp; &nbsp; <tt> 5 </tt>}}
<pre>
Line 1,574 ⟶ 1,573:
0.30902 -0.95106i
</pre>
{{out|output|text=&nbsp; when using the input of: &nbsp; &nbsp; <tt> 10 &nbsp; 36 </tt>}}
<pre>
───────────────────────10 roots of unity (showing 36 fractional decimal digits)
Line 1,588 ⟶ 1,587:
0.809016994374947424102293417182819059 -0.587785252292473129168705954639072769i
</pre>
{{out|output|text=&nbsp; when using the input of: &nbsp; &nbsp; <tt> -12 </tt>}}
 
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