Roots of a function: Difference between revisions

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=={{header|REXX}}==

~~The~~   '''bisection method'''   is used.

Both of REXX versions use the   '''bisection method'''   is used.

===function is coded as a REXX function===

<lang rexx>/*REXX program finds the roots of a specific function: x^3 - 3*x^2 + 2*x via bisection*/

parse arg bot top inc . /*obtain optional arguments from the CL*/

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found an exact root at 2

</pre>

===function is coded in-line===

This version is about 40% faster than the 1st REXX version.

<lang rexx>/*REXX program finds the roots of a specific function: x^3 - 3*x^2 + 2*x via bisection*/

parse arg bot top inc . /*obtain optional arguments from the CL*/

if bot=='' | bot=="," then bot= -5 /*Not specified? Then use the default.*/

if top=='' | top=="," then top= +5 /* " " " " " " */

if inc=='' | inc=="," then inc= .0001 /* " " " " " " */

x=bot-inc /*compute 1st value to start compares. */

z=x*(x*(x-3)+2) /*formula used ──► x^3 - 3x^2 + 2x */

!=sign(z) /*obtain the sign of the initial value.*/

do x=bot to top by inc /*traipse through the specified range. */

z=x*(x*(x-3)+2); $=sign(z) /*compute new value; obtain the sign. */

if z=0 then say 'found an exact root at' x/1

else if !\==$ then if !\==0 then say 'passed a root at' x/1

!=$ /*use the new sign for the next compare*/

end /*x*/ /*dividing by unity normalizes X [↑] */</lang>

{{out|output|text=  is the same as the 1st REXX version.}}

=={{header|Ring}}==