Ronald Luis Benvenutti <PICLIST@MITVMA.MIT.EDU> wrote:

> To solve the problem of SQRT calculation, I'm sending the following
> simpe routine I've been using for years.
> ....
> The routine does the following:
>
> It sums all odd numbers until the sum reaches the number 'n'. The
> number of iterations (sums) is the integer sqrt of 'n'.
>
> Is there something so simple ?

Ronald:

As Steve Hardy has pointed out, the routine as written is quite slow.
 However, it can be improved (at the expense of a little extra code
space) by performing a little pre-conditioning.  The following is the
QuickBASIC version of the square-root routine I posted here about a
year and a half ago; it uses the same algorithm as your routine, with
a few additional "if x = ...." lines at the start.

--------------------------------------------------------------------
rem Andy Warren's "Two Adds and a Subtract" Square-Root Finder.
rem 26 July 1994.
rem
rem For 16-bit radicands, this algorithm will make a maximum of 127
rem passes through the "mainloop" loop.  On average, it'll make 60
rem passes.  This seems like a lot, but each pass involves just one
rem 16-bit subtract (with a test for negative result), an 8-bit
rem increment, and an "add 2".
rem
rem For 16-bit radicands, "root" will always be in the range [0-255]
rem and "s" will always be in the range [1-511].

start:

    input "Radicand (0-65535): ";x

rem The following 6 "if" statements are included only for speed of
rem execution (they approximately double the average computation
rem speed).  They can be removed if program size is more important.

        if x > 16383 then x = x - 16384: root = 128: s = 257: goto main
        if x > 4095  then x = x - 4096:  root = 64:  s = 129: goto main
        if x > 1023  then x = x - 1024:  root = 32:  s = 65:  goto main
        if x > 255   then x = x - 256:   root = 16:  s = 33:  goto main
        if x > 63    then x = x - 64:    root = 8:   s = 17:  goto main
        if x > 15    then x = x - 16:    root = 4:   s = 9:   goto main

        root = 0: s = 1

main:

    x = x - s: if x < 0 then goto done

        root = root + 1: s = s + 2

        goto main

done:

    print "Square root = "; root: print

        goto start
-------------------------------------------------------------------

-Andy

Andrew Warren - fastfwd@ix.netcom.com
Fast Forward Engineering, Vista, California
http://www.geocities.com/SiliconValley/2499