Date : Thu, 02 Jun 2005 19:36:05 +1000 (EST)
From : Peter Craven <cjl_craves@...>
Subject: Re: Assembly Language Square Root
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Hi All
I have recently been searching for the fastest method to calculate the square
root of a 16-bit number.
I came across a Z80 Assembly Language program at the end of the web page at:
http://map.tni.nl/articles/mult_div_shifts.php
I have copied the relevant part:
(Snip)
Square root routine
This is a faster square root routine than the one previously given, test
results say that it’s 26% faster. It is written by Ricardo Bittencourt, so
many thanks to him :).
;
;Square root of 16-bit value
;In: HL = value
;Out: D = result (rounded down)
;
Sqr16: ld de,#0040
ld a,l
ld l,h
ld h,d
or a
ld b,8
Sqr16_Loop:
sbc hl,de
jr nc,Sqr16_Skip
add hl,de
Sqr16_Skip:
ccf
rl d
add a,a
adc hl,hl
add a,a
adc hl,hl
djnz Sqr16_Loop
ret
Well, that’s it. Thanks go to mr. Rodnay Zaks (although I somehow really
doubt he’ll read this) for writing his book “Programming of the Z80”, which
taught me about how to do multiplications on Z80, and has been the inspiration
for the routines listed here. If you have any suggestions for speed improvements,
or know of another method which might be faster under certain conditions,
please let me know.
~Grauw
(End Snip)
I have tried to 'translate' this into an assembly language program that can
be used by the Master computer:
10 l=&70:h=&71:d=&72;e=&73:a=&74
20 FORp=0TO1:P%=&B00:[OPTp*2
30 .sqr_root STZe:LDA#40:STAd:LDAl:STAa:LDAh:STAl:LDAe:
STAh:LDX#8:LDAa:ORAa
40.loop LDAl:SBCd:STAl:LDAh:SBCe:STAh:BCSskip:CLC:LDAl:
ADCd:STAl:LDAh:ADCe:STAh
50.skip BCSskip1:SEC:BRAskip2
60.skip1 CLC
70.skip2 ROLe:ROLa:ASLl:ROLh:ROLa:ASLl:ROLh:DEX:BNEloop:
RTS
80 ]:NEXT
90 INPUT"Enter number: "N%:!l=N%AND&FFFF
100 CALL&B00
110 PRINT ?e
However, this produces incorrect results, namely, if enter 100, results are
?l=220, ?h=170, ?d=40, ?e=128,
?a=17. If enter 1000, results are ?l=40, ?h=213,
?d=40, ?e=0,?a=0.
I have only recently briefly looked up how Z80 assembly language goes. Realise
'de' has 'd' as MSB and 'e' as LSB in the Z80, so when I swaped this in the
Master program, I hoped I have kept this consistent.
I have used the X register in the Master program because there is no 'b'
register that uses 'djnz'.
I realise that the first line could have simply put STZh instead of transferring
'e' memory location to it, but I tried to keep in line with the Z80 program.
Thought branching is quicker in regards to complementing the carry flag,
rather than playing around with the stack and the status, etc.
Thought it quicker to use ASL/ ROL instead of adding in line 70.
I really cannot work out what I have translated wrong, but assume my lack
of Z80 skills is the cause.
Can anybody help out??
Does anyone know of a quicker routine (not including Table)??
Further, would anyone be interested in having a monthlty 'competition' where
any topic is decided upon (eg. most interesting graphics design, weirdest
sounds, anything!!) and then a month is given for programs to be submitted,
and voted upon at end of month???
Programs could be in basic/ assembly language. Assume majority would rather
they work on Electron & BBC & Master...
Any takers??
Cheers
Pete
Dr Peter Craven (MBBS Uni. of Qld)
12 Treacher St
Mt Gravatt
QLD 4122
Ph (H): (07) 3349 0820
Send instant messages to your online friends http://au.messenger.yahoo.com
--0-1644151922-1117704965=:55952
<DIV>Hi All</DIV>
<DIV>I have recently been searching for the fastest method to calculate the
square root of a 16-bit number.</DIV>
<DIV> </DIV>
<DIV>I came across a Z80 Assembly Language program@... end of the web
page at: </DIV>
<DIV><A href="http://map.tni.nl/articles/mult_div_shifts.phphttp://map.tni.nl/articles/mult_div_shifts.php">http://map.tni.nl/articles/mult_div_shifts.php>
<DIV> </DIV>
<DIV>I have copied the relevant part:</DIV>
<DIV><BR><FONT color=#ff0000>(Snip)<BR></FONT><FONT color=#0000ff>Square
root routine</FONT></DIV>
<DIV><FONT color=#0000ff>This is a faster square root routine than the one
previously given, test results say that it’s 26% faster. It is written by
Ricardo Bittencourt, so many thanks to him :).</FONT></DIV>
<DIV><STRONG><FONT color=#00007f>;<BR>;Square root of 16-bit value<BR>;In:
HL = value<BR>;Out: D = result (rounded down)<BR>;<BR>Sqr16: ld
de,#0040<BR> ld a,l<BR> ld l,h<BR> ld h,d<BR> or a<BR> ld
b,8<BR>Sqr16_Loop:<BR> sbc hl,de<BR> jr nc,Sqr16_Skip<BR> add
hl,de<BR>Sqr16_Skip:<BR> ccf<BR> rl d<BR> add a,a<BR> adc
hl,hl<BR> add a,a<BR> adc hl,hl<BR> djnz Sqr16_Loop<BR> ret</FONT></STRONG></DIV>
<DIV><STRONG><FONT color=#00007f></FONT></STRONG> </DIV>
<DIV><FONT color=#0000ff>Well, that’s it. Thanks go to mr. Rodnay Zaks (although
I somehow really doubt he’ll read this) for writing his book “Programming
of the Z80”, which taught me about how to do multiplications on Z80, and
has been the inspiration for the routines listed here. If you have any suggestions
for speed improvements, or know of another method which might be faster under
certain conditions, please let me know.</FONT></DIV>
<DIV><FONT color=#0000ff>~Grauw</FONT></DIV>
<DIV><FONT color=#ff0000>(End Snip)</FONT></DIV>
<DIV><FONT color=#ff0000></FONT> </DIV>
<DIV>I have tried to 'translate' this into an assembly language program that
can be used by the Master computer:</DIV>
<DIV> </DIV>
<DIV><FONT face=courier color=#00bf60>10 l=&70:h=&71:d=&72;e=&73:a=&74</FONT></DIV>
<DIV><FONT face=Courier color=#00bf60></FONT> </DIV>
<DIV><FONT face=Courier color=#00bf60>20 FORp=0TO1:P%=&B00:[OPTp*2</FONT></DIV>
<DIV><FONT face=Courier color=#00bf60></FONT> </DIV>
<DIV><FONT face=Courier color=#00bf60>30 .sqr_root STZe:LDA#40:STAd:LDAl:STAa:LDAh:STAl:LDAe:</FONT></DIV>
<DIV><FONT face=Courier color=#00bf60>STAh:LDX#8:LDAa:ORAa</FONT></DIV>
<DIV><FONT face=Courier color=#00bf60></FONT> </DIV>
<DIV><FONT face=Courier color=#00bf60>40.loop LDAl:SBCd:STAl:LDAh:SBCe:STAh:BCSskip:CLC:LDAl:</FONT></DIV>
<DIV><FONT face=Courier color=#00bf60>ADCd:STAl:LDAh:ADCe:STAh</FONT></DIV>
<DIV><FONT face=Courier color=#00bf60></FONT> </DIV>
<DIV><FONT face=Courier color=#00bf60>50.skip BCSskip1:SEC:BRAskip2</FONT></DIV>
<DIV><FONT face=Courier color=#00bf60></FONT> </DIV>
<DIV><FONT face=Courier color=#00bf60>60.skip1 CLC</FONT></DIV>
<DIV><FONT face=Courier color=#00bf60></FONT> </DIV>
<DIV><FONT face=Courier color=#00bf60>70.skip2 ROLe:ROLa:ASLl:ROLh:ROLa:ASLl:ROLh:DEX:BNEloop:</FONT></DIV>
<DIV><FONT face=Courier color=#00bf60>RTS</FONT></DIV>
<DIV><FONT face=Courier color=#00bf60></FONT> </DIV>
<DIV><FONT face=Courier color=#00bf60>80 ]:NEXT</FONT></DIV>
<DIV><FONT face=Courier color=#00bf60></FONT> </DIV>
<DIV><FONT face=Courier color=#00bf60>90 INPUT"Enter number: "N%:!l=N%AND&FFFF</FONT></DIV>
<DIV><FONT face=Courier color=#00bf60></FONT> </DIV>
<DIV><FONT face=Courier color=#00bf60>100 CALL&B00</FONT></DIV>
<DIV><FONT face=Courier color=#00bf60></FONT> </DIV>
<DIV><FONT face=Courier color=#00bf60>110 PRINT ?e</FONT></DIV>
<DIV><FONT face=Courier color=#00bf60></FONT> </DIV>
<DIV><FONT face=Courier>However, this produces incorrect results, namely,
if enter 100, results are ?l=220, ?h=170, ?d=40, ?e=128, </FONT></DIV>
<DIV><FONT face=Courier>?a=17. If enter 1000, results are ?l=40, ?h=213,
</FONT></DIV>
<DIV><FONT face=Courier>?d=40, ?e=0,<FONT face=Courier>?a=0.<IMG src="http://us.i1.yimg.com/us.yimg.com/i/mesg/tsmileys2/31.gif">>
<DIV><FONT face=Courier></FONT> </DIV>
<DIV><FONT face=Courier>I have only recently briefly looked up how Z80 assembly
language goes. Realise 'de' has 'd' as MSB and 'e' as LSB in the Z80, so
when I swaped this in the Master program, I hoped I have kept this consistent.</FONT></DIV>
<DIV><FONT face=Courier></FONT> </DIV>
<DIV><FONT face=Courier>I have used the X register in the Master program
because there is no 'b' register that uses 'djnz'.</FONT></DIV>
<DIV><FONT face=Courier></FONT> </DIV>
<DIV><FONT face=Courier>I realise that the first line could have simply put
STZh instead of transferring 'e' memory location to it, but I tried to keep
in line with the Z80 program.</FONT></DIV>
<DIV><FONT face=Courier></FONT> </DIV>
<DIV><FONT face=Courier>Thought branching is quicker in regards to complementing
the carry flag, rather than playing around with the stack and the status,
etc.</FONT></DIV>
<DIV><FONT face=Courier></FONT> </DIV>
<DIV><FONT face=Courier>Thought it quicker to use ASL/ ROL instead of adding
in line 70.</FONT></DIV>
<DIV><FONT face=Courier></FONT> </DIV>
<DIV><FONT face=Courier>I really cannot work out what I have translated wrong,
but assume my lack of Z80 skills is the cause.</FONT></DIV>
<DIV><FONT face=Courier></FONT> </DIV>
<DIV><FONT face=Courier color=#ff0000 size=5><STRONG>Can anybody help out??</STRONG></FONT></DIV>
<DIV><STRONG><FONT face=Courier color=#ff0000 size=5></FONT></STRONG> </DIV>
<DIV><STRONG><FONT face=Courier color=#ff0000 size=5>Does anyone know of
a quicker routine (not including Table)??</FONT></STRONG></DIV>
<DIV><FONT face=Courier></FONT> </DIV>
<DIV><FONT face=Courier><FONT color=#00bf60 size=6><FONT style="BACKGROUND-COLOR:
#ffff00">Further</FONT>, would anyone be interested in having a monthlty
'competition' where any topic is decided upon (eg. most interesting graphics
design, weirdest sounds, anything!!) and then a month is given for programs
to be submitted, and voted upon@... of month???</FONT></FONT></DIV>
<DIV><FONT face=Courier><FONT color=#00bf60 size=6></FONT></FONT> </DIV>
<DIV><FONT face=Courier><FONT color=#00bf60 size=6>Programs could be in basic/
assembly language. Assume majority would rather they work on Electron &
BBC & Master...</FONT></FONT></DIV>
<DIV><FONT face=Courier><FONT color=#00bf60 size=6></FONT></FONT> </DIV>
<DIV><FONT face=Courier><FONT color=#00bf60 size=6>Any takers??</FONT></FONT></DIV>
<DIV><FONT face=Courier><FONT color=#00bf60 size=6></FONT></FONT> </DIV>
<DIV><FONT face=Courier><FONT color=#00bf60 size=6>Cheers</FONT></FONT></DIV>
<DIV><FONT face=Courier><FONT color=#00bf60 size=6></FONT></FONT> </DIV>
<DIV><FONT face=Courier><FONT color=#00bf60 size=6>Pete</FONT></DIV></FONT><BR><BR><DIV>
<DIV>
<DIV>
<DIV>
<DIV>
<DIV>
<P>Dr Peter Craven (MBBS Uni. of Qld)</P>
<P>12 Treacher St</P>
<P>Mt Gravatt</P>
<P>QLD 4122</P>
<P>Ph (H): (07) 3349 0820</P></DIV></DIV></DIV></DIV></DIV></DIV><p>Send
instant messages to your online friends http://au.messenger.yahoo.com
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