Re: Decimal versus binary arithmetic was Re: J4 - presentation/discussion on "Fu

On Tue, 01 Apr 2008 19:29:05 -0300 Clark F Morris <cfmpublic@ns.sympatico.ca
>
wrote:

:>On Tue, 1 Apr 2008 13:14:46 -0600, "Frank Swarbrick"
:><Frank.Swarbrick@efirstbank.com> wrote:

:>>>>> On 4/1/2008 at 12:43 PM, in message
:>><if05v3503beg04nonbeci3n8eqo2vill79@4ax.com>, Clark F
:>>Morris<cfmpublic@ns.sympatico.ca> wrote:
:>>> On Mon, 31 Mar 2008 22:37:12 -0600, Robert <no@e.mail> wrote:

:>>>>On Mon, 31 Mar 2008 21:55:10 -0300, Clark F Morris
:>>><cfmpublic@ns.sympatico.ca> wrote:

:>>>>>On Tue, 18 Mar 2008 19:34:51 -0600, Robert <no@e.mail> wrote:

:>>>>>>Lots of muddled thinking on numeric errors has been published. Some t
alk
:>>> about 'binary
:>>>>>>arithmetic' without making a distinction between integer and floating
:>>> point. Here's an
:>>>>>>example:
:>>>>>Try doing a simple divide like calculate the value of 1 / 5 in binary.

:>>>>OK.

:>>>>01  numerator value 1 binary pic 9(9).
:>>>>01  denominator value 5 binary pic 9(9).
:>>>>01  quotient binary pic 9(9)v9(4).

:>>>>compute quotient = numerator / denominator
:>>>>display quotient

:>>>>0000000002000

:>>>>>You get a never ending fraction.

:>>>>Looks pretty diadic to me.
:>>> You may have to do this in Assembler to get the results that I am
:>>> talking about.  Take a look at the generated instructions.  If I had
:>>> access to an IBM mainframe I would compile a small test program to see
:>>> what the underlying code is.

:>>5820 9510               L    2,1296(0,9)             NUMERATOR
:>>4E20 D1C4               CVD  2,452(0,13)             TS2=4
:>>D203 D1C0 C02A          MVC  448(4,13),42(12)        TS2=0
:>>          SYSLIT AT +42
:>>F060 D1C5 0004          SRP  453(7,13),4(0),0        TS2=5
:>>5820 9518               L    2,1304(0,9)             DENOMINATOR
:>>4E20 D1D0               CVD  2,464(0,13)             TS2=16
:>>FDB4 D1C0 D1D3          DP   448(12,13),467(5,13)    TS2=0
:>>          TS2=19
:>>F896 D1E0 D1C0          ZAP  480(10,13),448(7,13)    TS2=32
:>>          TS2=0
:>>960F D1E9               OI   489(13),X'0F'           TS2=41
:>>D202 D1D8 C02A          MVC  472(3,13),42(12)        TS2=24
:>>          SYSLIT AT +42
:>>D204 D1DB D1E5          MVC  475(5,13),485(13)       TS2=27
:>>          TS2=37
:>>4F20 D1D8               CVB  2,472(0,13)             TS2=24
:>>F144 D1DB D1E0          MVO  475(5,13),480(5,13)     TS2=27
:>>          TS2=32
:>>4F50 D1D8               CVB  5,472(0,13)             TS2=24
:>>5C40 C004               M    4,4(0,12)               SYSLIT AT +4
:>>1E52                    ALR  5,2
:>>58B0 C034               L    11,52(0,12)             PBL=1
:>>47C0 B698               BC   12,1688(0,11)           GN=16(000A70)
:>>5A40 C000               A    4,0(0,12)               SYSLIT AT +0
:>>               GN=16    EQU  *
:>>1222                    LTR  2,2
:>>47B0 B6A2               BC   11,1698(0,11)           GN=17(000A7A)
:>>5B40 C000               S    4,0(0,12)               SYSLIT AT +0
:>>               GN=17    EQU  *
:>>9045 9520               STM  4,5,1312(9)             QUOTIENT

:>Wow, they are actually doing this in decimal.  I wonder what the code
:>would be like using binary instructions.  I see they are handling the
:>remainder separately.

I would guess the conversions are being done to properly handle the differen
t
scaling factors, where decimal arithmetic can handle larger precisions
(fullword is limited to 10 digits while packed can hold 15 digits - and with
 Z
hardware, the numbers double).

Try them all with the same picture, 9(4)V4(9), which will fit in a word.

--
Binyamin Dissen <bdissen@dissensoftware.com>
http://www.dissensoftware.com

Director, Dissen Software, Bar & Grill - Israel


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