DTACK GROUNDED #15
November-December 1982
DTACK GROUNDED, The Journal of Simple 68000 Systems
Issue # 15 November-December 1982 Copyright Digital Acoustics, Inc.
PHASE ZERO REPORT:
Here is a letter received from Phase Zero along with a disk: "Enclosed is an updated version of ASSEM68K. Problems with MOVEQ, MOVEM, LIST, and TRUNC instructions and the .L addressing mode have been fixed (we didn't know about those last two - ed).
"Although we are sending letters to all of our past customers, we would appreciate your mentioning in DTACK GROUNDED, that we will supply this update at no cost. If they will return their original disks to Phase Zero, the revision will be returned promptly."
Consider it mentioned, Dan.
THE DYNAMIC RAM BOARD DESIGN is being finalized AND BLACK TAPE IS BEING LAID ON CLEAR ACETATE. When we reach that last stage, we consider construction under way here at Digital Acoustics. The board will be a 636K MX-80 printer buffer which just happens to have a 68000 an board. You see, all 68000 boards MUST come with incredibly complex operating systems but printer buffers are just a functional utility piece of hardware (and we might want to advertise in BYTE).
Speed is not finalized but we are leaning to a 12.5MHz CPU with one wait state. Refresh is by software assisted by hardware; overhead about 3%. Because of refresh interrupt no timing-critical software can be written and FULL HANDSHAKE must be used by the 6502 at all times (not true of existing 6502 utility software).
636K = five rows of sixteen each 64K DRAMs less 4K at the start of memory to match the existing DTACK board. No provision for parity, hence name is MELKEN, not Dtack Grounded. DTACK is NOT grounded on the MELKEN. Board size identical to Dtack, identical interface & expansion connectors.
Identical size to use real DTACK enclosure which we will really have some day manana.
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To be sold with 1, 2, 3, 4 or 5 rows of DRAMs. Price not yet determined, but (sigh) we HAVE taken a closer look and 252K might be a little over $1K. We COULD sell it for $1K if we didn't want to make a profit, but we do not think the stockholders would go along with that.
MELKEN? Hint: The following quotation has been attributed to H. L. Menken: "Nobody has ever lost a dollar underestimating the taste of the American public."
This board will be suitable for:
- Those people who want a really big printer buffer.
- Those people who have all of their slots filled but still want a 68000 to play with. Printer buffers plug into slot 1, right?
- Those people who do not care about maximum speed, who do not need to write time-crucial software (such as a 68K RWTS) and who can tolerate an occasional bit error because of the nature of their application.
- The dummies who think dynamic RAM never has errors. (If they are THAT dumb, somebody is going to take their money and it might as well be us.)
WE BUILD THE DTACK BOARDS so that we can have a high quality and high performance product in which we can take pride. We are going to build the MELKENs because we have greedy stockholders. ARS GRATIA PECUNIA. Besides, our Quadram 64K print buffer gets full if a source listing has more than 1300 lines so we need a bigger print buffer.
ISN'T PROGRESS WONDERFUL? We have long had home trash compactors which will magically transform 13 pounds of garbage into 13 pounds of garbage. Now we can also have a print buffer which will reduce the time to print a long source listing from 48 minutes to 48 minutes.
OPERATING SYSTEMS:
We were certainly naive when we covered the various kinds of operating systems using only two pages in newsletter #10, including a quarter page on UNIX. Having COMPLETELY disposed of the matter we naturally had to expend another page on UNIX in the last issue.
The subject just won't go away. All one reads about in the magazines is comparisons of operating systems. Unfortunately some of those who are writing about the subject don't know much about it. What is even worse is that people are picking up buzzwords like UNIX. An Atari owner gets tired of shooting rocks for awhile and picks up a personal computer magazine which asserts that UNIX is a wonderful operating system (true) and therefore HE, the rock-shooter, wants and needs UNIX. RIDICULOUS!
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We are sure that all of our readers are aware that BYTE magazine is the leading publication for personal computers (above the rock-shooting level). You know, because we called it to your attention recently, that NONE of those 100 vendors of stand-alone 68000 systems advertised in MICRO's special 68000 edition. You probably think that there are lots of 60000 systems advertised in BYTE. Well, there are a heck of a lot MORE that DON'T advertise in BYTE.
So where DO those other 68000 system vendors advertise? Publications like COMPUTER DECISIONS, COMPUTER DESIGN, DATA COMMUNICATIONS, DATAMATION, DIGITAL DESIGN and INFOSYSTEMS. But the flagship publication of this group, as measured by advertising pages (which is surely how we measure BYTE) is MINI-MICRO SYSTEMS. These publications are favored by those vendors who are coming after you and thirty-one of your fellow workers with chains and shackles to chain ALL of you to ONE crummy little microprocessor. The 68000 and UNIX are quite popular among this group. You will never, ever read anything in MINI-MICRO about single user systems. Well, almost never.
In their Aug. '82 issue MINI-MICRO ran an article on desktop personal computers and had to explain to their readers what these things are, we kid you not. MINI-MICRO dismisses the Apple Computer Co. as having pioneered mass marketing of small business computers (in other words, made all the mistakes) so that IBM would know how to do the job. Read Sep '82 pp 122 and 127.
We assume that none of our readers wish to be shackled to one of thirty-two work stations. Unfortunately, that is exactly what most vendors of 68000-based systems want to do to you.
In this newsletter we tell you how such nicer it is to have a microprocessor with 20 units of speed instead of one unit. In MINI-MICRO you learn how much nicer it is to market $200 million worth of workstations instead of a mere $10 million. We are oriented to the individual computer owner/operator. We are not absolutely certain what MINI-MICRO's attitude toward a PET/APPLE owner is, but we suggest that you carry an umbrella if you are going to stand on the sidewalk under their editorial offices.
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It seems that as soon as a microprocessor is developed with minicomputer computational capability that the minicomputer boys move in and try to apply it just like the PDP11/70 was applied in the 1970s. Now can we (you and us) move up to a modern, high-performance microprocessor in a personal computer? Surely the individual computer owner/operator is not to be condemned to a 6502/Z80 ghetto?
True, one answer to those questions is a bit self-serving. But there are others, such as the SAGE (which no longer claims 2 MIPS performance in its recent ads). It does still advertise a $3995 price tag, which is true if you already own a Televideo 925 terminal and can get by with one tiny disk drive, equivalent to an Apple Disk II. But if you buy the terminal and get two floppy disks with USEFUL storage capacity you are at about $5700.
However, it appears that the SAGE system is aimed at the single user and that's us. We don't know such more about the system (would a reader contribute a review?) except the fact that the console is a terminal, which means no HIRES graphics in the Apple II sense and also means that there is no memory-mapped text; the screen will instead be filled at RS-232 rates, presumably 9600 baud. It takes two full seconds at that transmission rate to fill a 24 X 80 screen.
There are some things that one just does not give up after trying them. After switching from cassette to floppy disks one does NOT go back. After having a 24 X 80 CRT with upper-lower case with true descenders, one does NOT go back to a crude 40 column screen with upper case only (which is why this is being keyed on a CBM 8032, NOT an Apple II). And having had HIRES graphics available one does NOT give them up. There is an Apple II sitting five feet from your FNE as he keys this.
For this reason, we do not think many Apple owners are going to switch to the SAGE. It might be attractive to a CBM 8032 owner, however. If you like terminals, the Televideo 925 is an outstanding unit in its price range.
Our personal favorite prospect (we really do not have much detailed information on it) is the Corvus Concept. This is really intended as a work-station (faugh!) but it can be configured as a personal computer by adding floppy disks, taking the price to about $7000. That is NOT cheap! But it has absolutely LOVELY graphics capability: 720 by 560 pixels! In case you are not paying attention, that has the correct 'aspect ratio' so that a plot of 100 pixels horizontally is exactly as long as 100 pixels plotted vertically. We love it!
What we do not know is whether there is (or will be) a good single-user operating system and a good BASIC. Corvus has announced very little software for that machine even in its work-station guise. BUT: 720 by 560!
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GOOD NEWS DEPT:
Motorola has fixed the 12.5 MHz bug, in engineering at least, and will be back in production towards the end of Nov. That sounds like about the time required to move new masks into production. If we assume about two or three weeks to fill the pipeline from the factory to us via distributors, we should be back in the 12.5 MHz business right around HO! HO! HO! time.
Since we get very little done between Xmas and the New Year, if you have one of our TEMP-8 boards, hold onto it so you mill have something to play with over the holidays and then send it in for upgrading early in January. If we get L12's earlier than expected, we will send individual notices to TEMP-8 board owners.
MISCELLANEAE:
IN DEC. '82 CREATIVE COMPUTING MAGAZINE there is an article on a bunch of foreign processor boards for the Apple II which includes our little jewel. We realize, of course, that none of our readers would stoop to subscribing to that rag, so go next door and steal your neighbor's kid's copy. The article is in the page 30 to 40 area.
Perhaps the most interesting thing is that Mike Coffey, C.C.'s technical editor, tried our Dtack board WITH that 3.58 MHz 6502 board by Number Nine. They worked well together and in fact that combination was by far the fastest for the benchmarks tested. Mike also reported that observers were impressed by "a three dimensional demonstration graphics program growing on the screen in real time... but nobody volunteered to duplicate it!"
FADING MEMORIES is the lead for an article from Oct. 18 Electronic News. It seems that some of the minicomputer manufacturers (our very favorite persons) are finally dropping add-on memory prices now that inexpensive 64K RAM chips are here. Wang is charging $16K per megabyte and DEC is down to $9K for one megabyte. Those are the NEW, LOW prices folks! Let's see, now: that means we should price our 5/8 megabyte board at over $5,000 just for the RAM alone and then another $500 or so for the 68000, interface board, software and documentation.
How many of you will pay us $5,645 for our 636K print buffer? PLEASE! sir, there are ladies present!
In the meantime our 10 year old Wang 2200C is getting seriously in need of being taken behind the barn and shot. Unfortunately, that would leave us with over a hundred 8 inch floppy disks filled with useful software. So we checked with the Wang sales office and sure enough they still make a 2200, with the latest version called the SVP. For $6200 we can get a single-user computer complete with terminal and two double-sided double-density 8 inch drives. One megabyte per drive, two megabytes total on line.
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$6200 is the price with 32K user memory. To add another 32K costs another $1200!!! That's right, they are charging $1200 for 16 each SIXTEEN 16 K DRAMs! Those 16K chips are less than a buck each right now. And since their monthly maintenance fee is a percentage of the sale price, they will charge another sixteen bucks a month to maintain those RAMS. In other words, you pay $1200 up front and still have to re-purchase the RAMs each and every month!
If you want to upgrade again, this time from 64K to 128K those good-hearted people want ANOTHER $1200.
The SVP 2200 is, we believe, a 2901 bit-slice machine. The BASIC is microprogrammed, not interpreted in the usual microcomputer fashion. As a result it is a very fast machine, about 40% the speed of our 12.5 MHz board or about the same speed as Motorola's $28,900 EXORMACS. At $6200 including two big floppies it is a bargain. But those people need a mask and a gun when it comes to memory upgrades!
WAYNE GREEN WATCH: In our last issue we told you about '80micro's report that only 2000 Tandy Model 16s had been sold, and that most of those were sitting on dealer's shelves. You MAY have noticed that we did not personally endorse that report. What we DIDN'T tell you is that same issue carried numerous references to a feud that Wayne is having with Jon Shirley, who is Radio Shick's sales honcho for bit-bangers. Of course, Wayne is almost always feuding with someone.
The background for the feud with Jon Shirley is that Radio Shack does not repeat not want foreign parts/boards attached to Radio Shack microcomputers. Since Wayne publishes a magazine which features numerous advertisements for foreign enhancements there is an obvious and immediate conflict in which each participant deeply feels that HE is on the side of the angels.
But one does not really need to have a logical basis to feud with Wayne Green; ask Jim Warren for instance.
Anyhow, our sources tell us the Model 16 is selling well despite the ABSOLUTE TOTAL ABSENCE of software for the 68000. Here are the reasons: 1) The Model 16 is priced only a little higher than the Model II; and both machines sell to businesses, not hackers, go the price is much less sensitive, and besides there MIGHT be some software someday, right? 2) You can get TWO 8 inch drives in the console of the 16 but only ONE in the Model II. This provides a VERY strong incentive to buy the Model 16.
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In any event Tandy's small computer sales climbed from $369 million to $624 million in its fiscal year which just ended. And they say that the Model II and the Model 16 accounted for over a quarter of that, or $160 million. Sounds like more than 2000 Model 16s to us! (Now if only the 68000 in all those computers could do something useful ... )
SCHIZOPHRENIA DEPT:
You may have seen a mention on page 476 of Oct '82 BYTE of a 68000 board by a company called Intellimac. The board is called the MAGNUM 68. The product release stated that it has a 6MHz operating speed, 8MHz optional. Optionally available is an EPROM-resident extended BASIC. 256K DRAMs and Pascal are also available as options. The price for the board and a manual is $745.
The very same company has a full page ad which is running in several publications. We have seen it in one of the electronics hardware mags, EDN we think, and it can also be found on page 46 of Sep '82 MINI-MICRO (how in the world are they going to tie 32 users to that little board?). This advertisement mentions no software except the monitor/debugger which is MACSBUG flavored. The advertisement asserts that the system uses a 6MHz 68000 and cases with a 100+ page manual.
The first product release we saw in trade journals listed the board at $895 (as we recall). When we saw a product release several weeks later for the same board at $745 we decided to take a look-see and arranged for another small company to purchase one for us. Delivery was prompt. Since we HAVE one of these boards, let us tell you about it.
First, the construction is absolutely superb. We cannot ever recall seeing at first hand a product in the personal computer field with equivalent quality. It is a four-layer board and the layout was clearly done using a CAD program and digital platter. The LSTTL parts are hard-soldered to the board and the MOS LSI parts are socketed. The board is obviously designed for automated production. There is no evidence of hand workmanship on our board.
The shipper which arrived with the board stated that the board was serial number one. On the bottom of the board was a paper sticker (Avery label variety) which was almost falling off. The sticker explained that the board was serial number 2 and that the warranty was void if the sticker was removed. There was a 100 page manual which uses large print, lots of double spacing, lots of white space and large illustrations. Page 15 has three lines of print.
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On page 14 we find the following statement:
SYSTEM CLOCK: 8-MHz crystal providing 4-MHz processor operations.
The board they shipped us, whether serial number 1 or 2, has an 8MHz crystal which provides a 4MHz clock signal to pin 15 (CLK) on the 68000, which is a Hitachi HD68000-6. See, they're telling the truth about using a 6MHz CPU in their full page ad. Sure wish it ran at 6MHz. It does have 128K of DRAM. Oh, yes: the board is not expandable in any way.
The board can communicate with a host computer via RS-232 at a maximum rate of 9600 baud, or about 1000 bytes per second. This compares to a data transfer rate of 71,000 bytes per second for our DTACK board, and that is a host-cpu limitation. However, those persons who criticised our board early on will love the Magnus 68; it has TWO RS-232 ports!
The introduction to the manual states that "The 68 MAGNUM has been developed as... an educational tool... ." It certainly will be educational! The board comes with absolutely NO demonstration or utility software listings. Although there is that MACSBUG look-alike in EPROM(s), no listing is provided for that monitor. The user is TOTALLY on his/her own.
Those advertised descriptions do not appear to match the board that we have in hand in all respects. But if you have $745 to spare you can buy a fantastically well made 68000 board which runs somewhere between 4 and 8 MHz and which comes with absolutely no software.
Would the real MAGNUM 68 please stand up?
We got into a very childish "my old man can lick your old man" argument with the vice-president of a software house back on the east coast the other day. Each of us was asserting that his respective company would be absolutely the FIRST to introduce working hardware coupling the National 16081 math chip to the 68000. Which is very interesting because we are a hardware manufacturer but the software house has NOT been, up to now. The vice president dropped a couple of hints that eight lead one to believe that they are working on something close to a TRASH 68, which as you will recall is what we think this industry badly needs.
If that software house really brings out a TRASH 68, or does the level 1/3 BASIC and crummy operating system for a manufacturer of a TRASH 68, we will have to apologize for saying we could hit the market with hardware first. Even if it's true.
And is it remotely possible that there is a connection between the software house and Intellimac?
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ASM BUG REPORT:
The six instructions 'XXXI' (e,g, ADDI) do not assemble correctly using our utility program 'ASM', alias 'Hand Assembler's Helper'. In the Apple version, shorten line 2210 by adding line 2212 and move the last three statements in line 2210 to this new line. Then retype line 2210, inserting "L1=L:L=0:" after 'GOSUB 310:' (but less the three statements which have been moved to the next line).
The fix for the Pet version is the same, except that it is line 2260 which must be changed, inserting "l1=l:l=0" after 'gosub 400:'. First move the last three statements to new line 2262 since this addition will make the line too long for the screen editor.
We have known all along that 'MOVEP' is not implemented. That instruction can't be used with the DTACK board, so we left it off on purpose. We have just now learned, thanks to a diligent reader who has written us TWICE, that we overlooked 'LEA'. He also informs us that the printer option does not work with some variations of the 'MOVE' instruction. Since there are thousands of variations, it would help if he was a little more specific.
(We vigorously deny his assertion that we do not power up our boards before testing them. He was referring to the report of the wire stuck under the sockets. What happened was we had a number of tested boards with various memory sizes racked on their side in a 'desk organizer' located in the production area. A cut resistor lead flew into the air and fell on the board just right (?) to stick under the sockets. When the order came in for that size board, we shipped it.)
Of the various forms of the 'decrement and branch' instruction, the only one we implemented was 'DBF'. This oversight on our part was originally pointed out to us by John Martellaro of Peelings II magazine.
According to a letter from Oliver B. of Hamburg, W. Germany the MOVE (PC)+d and MOVE (PC)+R+d addressing modes do not work. Either Oliver has a VERY old copy of program ASM or he is confused over source versus destination addressing modes. While ALL addressing modes are legal as the source operand for instruction MOVE, only data alterable addressing modes are legal for the destination operand. See page 133 of Motorola's User Manual (3rd Edition) or page B-45 of the 2nd Edition.
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WATCH THOSE GOTCHAS!
In the last newsletter we said that ADDQ and SUBQ work with address registers as well as data registers. That happens to be true. We also said on page 5 that DO SOMETHING, SUBQ #1 An, BNE DO SOMETHING will work. According to the 2nd edition of the User Manual that's true. See page B-80. Unfortunately, when we tried code like that recently it didn't work. After three hour's wrangling we thought to check the 3rd Edition. Page 174 tells you that the flags are NOT set after a SUBQ. Not only that but after a SUBQ.W #x,An the result will be sign extended into the upper 16 bits of the address register.
Mind you, ADDQ and SUBQ DO work with the address registers, but it is important to know exactly HOW they work. So go out and get a 3rd Edition if you do not already have one.
You can't believe everything in the 3rd Edition either. See the bottom of page 188 where it states that (for TST) a size field of 11 = long word. Uh uh, try 10 = long word instead. (We forget who called this to our attention.)
MORE BUGS YET: For you Apple types, there is a bug in UTIL4 sent out in update #3 that we have just identified. The problem is that three groups of three bytes each are in reverse order. Make these changes in text file U4.S using DOS Toolkit's editor:
line 134: DFB $A0,DB
135: DFB $A9
line 146: DFB $EB,$21,
147: DFB $20
line 149: DFB $48,$A2
150: DFB $A5
Now we need to modify working binary file "UTIL4". Load program "SETUP"; make sure line 20 loads UTIL4, and run the program. This places the binary file in memory. If UTIL4 is locked, unlock it.
Enter the monitor using CALL-151. Modify the three locations by typing these lines:
8EBB: A0 DB A9 (RETURN)
8ECF: EB 21 20 (RETURN)
8ED4: 48 A2 A5 (RETURN)
THE SPACES IN THOSE LINES ARE VERY IMPORTANT! Return to BASIC by keying 3D0G (RETURN) and key in this line:
BSAVEUTIL4,A$8600,L$1000
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Finally, lock the file if you wish.
What these bugs would do if not fixed is trash the EXP, TAN and ATN functions IF you had first linked into the Applesoft floating point routines by first CALLing 38383 and THEN de-linked back to the 6502 by CALLing 38380. The bugs are in the de-linking code.
Since we thoroughly tested those routines by comparing the results against the Microsoft calculations for the same random operands, how did this bug sneak through? We performed those tests on our CBM 8032. With an 80 column screen and a screen editor (you Apple types don't know what you are missing) it is MUCH easier to debug 68000 code than on the Apple where every program line must be re-typed in its entirety!
One of our readers has committed the horrible mistake of asserting that your FNE exhibits evidence of literary ability. This is such like telling a 14 year old girl that she is a great actress! So, all of you will have to bear the consequences: following is our brief (thank heavens!) outline of The Great American Novel, silicon gulch variety.
Let's see, now: a novel requires sex, violence, conflict and some other stuff that we forget for the moment. So we start the novel off by telling about this wonderful personal computer firm that started in a garage. You easterners who wonder why those computer firms never start in a basement are advised that there ARE no basements in California. Where were we?
Oh, yes. Well, these two guys start up this personal computer firm and build it up until the sales are quite a few million bucks a year. But one of them has started an affair with the other's wife, and gets caught in flagrante delecto by his partner with permanently fatal results.
In Texas that may be legal grounds for killing off your partner but California has a more laid-back life style and the D.A. puts a warrant out on the guy. He sensibly splits permanently for Peru after cleaning out his various bank accounts. The two wives are not technical types and they sell out to a conglomerate which re-names the outfit the ACME Computer Co. and the wives prepare to spend the rest of their lives clipping coupons in the beauty parlor. All this stuff happens in flash-back format and the story really starts after ACME takes over.
But it gives us a swell shot at some sex and violence right at the start of the book so browsers will get hooked and take the book home. Look, you can sell the 1949 Gdansk telephone directory if the first five pages have some steamy sex scenes.
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It turns out those two guys had designed a dynamite computer and sales continued to climb rapidly for a couple years after they departed (one for Peru, the other's destination questionable but the possibilities heavily weighted considering the circumstances). After a while the new managers look around and start talking about designing a computer themselves; they aren't getting any respect from their peers (the Honchos of the other computer makers) by making big dough off those two guys' design.
The new managers announce to the world that the world's absolute greatest ever personal computer will be forthcoming from the ACME Computer Co. and that you had better believe it. So they set up a 40 person design team and gave them the word to fulfill that claim. So those 40 guys set to work. (Linda, you will not mind the inference that they were all sale type persons when you see how this comes out.)
They made this computer which, when you pushed the integrated circuits into the sockets, the sockets popped them right back out again. They cleverly designed the package so that there were two completely enclosed areas, as in completely enclosed within an aluminum casting so the air could not move. Now, fiberglass and foam are excellent thermal insulators because they trap lots of air so that the air can't move. When air doesn't move the heat doesn't move either. So there they had this computer with parts that normally run hot such as bipolar ROMS and PLAs and such locked into completely enclosed compartments where the air couldn't move. And they were surprised when the parts overheated and the computer would, forthwith, fail. They built an emulation mode so that the wonderful new computer could run software written for the old computer which was not designed by ACME engineers. Naturally, the emulation mode did not work. Oh, yes: they built in a real time clock which, of course, did not work.
So when the world's absolute greatest ever personal computer was released to the public it drew, well, mixed reviews. Actually, they weren't mixed reviews, they were all negative. Actually, they weren't negative, they were... you get the idea.
Back in the board room at ACME there was a meeting at which much spleen was vented (how does one vent spleen?). A resolution was introduced which stated clearly that the fault was not at the high executive levels within ACME management (it passed unanimously). The vice president in charge of production suggests that those engineers who made serious design mistakes be identified and terminated. They would then be replaced by competent types who would rectify (dirty word? check dictionary) the problems.
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The V.P. marketing points out that it would be a shame to blot an engineer's reputation for life by identifying his as personally having made a serious mistake. It would, asserted the V.P., be much more humane to simply terminate all 40 of the development team responsible for the debacle and concomitant dimunition (check the vocabularity!) of the reputations of the upper management of ACME. So that's what they did.
They brought in new engineering talent which put bandaids over some of the problems, fixed some of the problems, and ignored some of the problems as insoluble.
This being sort of accomplished, ACME management split up the new talent, added to it, and began development of not one, not two, but THREE more world-beaters. Time passed, monies were spent and prototypes and production prototypes and pilot production runs ensued (came forth? were constructed? make note to hire ghost). The upper aelerons of ACNE management anxiously waited for word that these new products were ready for introduction. And waited. And...
Well, that word just never came. So the V.P. R & D personally descended from the board room to ascertain the nature of the difficulty, if any. At each of the three groups he discovered that the software was not thoroughly debugged, life testing of the hardware was underway but was incomplete, and well, like that. Since each group had had much more time than needed to do the job, this proved puzzling. So he reported back to the board room that the new products were not ready for introduction. Which they knew already.
Several months passed and the V.P. R & D was sent forth to see to it that those products got introduced immediately! The development groups reported that tests were incomplete. One group pointed out that they were almost certain that a 7400 NAND gate could turn into a NOR gate under certain conditions and that they were exhaustively testing to confirm or disprove this hypothesis. In other words, the development groups were foot-dragging, obfuscating and stonewalling.
Why were the development teats doing this, you may ask? Because they were logical per, um, because they had learned from hist, ah HERE'S the reason, dammit: One of the development group leaders had studied the mistakes of the first engineering group. Here is what he deduced:
- Before the new product was released all of them had jobs.
- After the new product was released none of them had jobs.
- The reason they lost their jobs was that the product was released.
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This group leader discussed the situation with the other two team leaders. They:
- Agreed that none of their new products had been released and noted that they and their teams were still employed.
- Agreed that this could be a coincidence.
- Agreed that termination of employment was not necessarily imminent upon release of their new products.
- Agreed that, nevertheless, 100% (1 out of 1) of all of the new product development teams which had released their new design under present ACME management had been terminated en mass.
- Agreed that they each and severally had orthodontist's bills and mortgage payments to meet and various and sundry other bills to pay and that the other team members, which they were really thinking about of course, had bills to pay too.
- Agreed that under conditions created entirely by present ACME management that releasing their new products would be foolhardy to say the least.
We are kind of stuck at this point in our plot since it seems that ACME management is going to have a strong desire to release something to appease the stockholders and their retail outlets and their stock analysts and enhance their prestige in their peer group and... you get the idea. And the poor engineering groups still have those orthodontist bills to pay. And so nothing is being released which doesn't make sense since the boss is the boss or isn't they?
As soon as this little glitch in the plot gets cleared up we will submit this outline to the more prestigious publishers and begin the first actual draft as soon is we get our $500,000 advance. And all of you will be pleased to be able to say that you read your FNE's work back before he was rich and famous.
What's that? You say that is the dumbest way to run a company that you have ever heard of? Look, pal: novels are FICTIONAL, and this is a novel. If novels were written like real life they would bore you to tears.
Maybe it was the pepperoni pizza, chili and ice cream but against our better judgement we have finally written something sort of related to software piracy in the next two pages. If you have any sense at all you will skip those next two pages. (If we had any sense at all we would have taken a cold shover instead.)
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ETHICS AND COMMERCE:
A possible application for our (eventual) 68008 Apple board would be as a supercharger for the popular electronic spreadsheet. Now, that particular program is locked and it ALSO uses its OWN floating point package. So our standard utility won't work because it speeds up the Applesoft floating point but that program does not use Applesoft's floating point.
Which means that we need to be able to 'unlock' that software package to identify the floating point package format and the entrance points to the various routines just as we have done for the Apple and Pet. Do we then provide the software package with those modifications? No, we do not own that software and we cannot sell it or even give it away. What we CAN sell or give away is the modifications themselves along with the 68000 code to enhance (speed up) the package.
Naturally, it is extremely difficult to break a locked software package. Ahem. Like you, we have NEVER, EVER heard of something called an NMI. But there is an easier way.
You see, we intend that the 68008 card have DMA capability (which the big DTACK board doesn't). If you have DNA capability you can load any locked software whatever into the Apple and let the DMA device read it out! There are various ways to store the code; we had in mind sending it via (emulated) RS232 to a second processor. Emulated means that the timing of the signal is RS232 but the connector does not have 25 pins and the signal swings are TTL.
We would then provide the 'hooks' to the electronic spreadsheet program pretty much in the same form as our existing enhancement code. Except that the modifications would be done via DMA without the 6502 knowing what had happened.
The ethical problem we were having was, do we tell people how to do this? The possibilities for mis-use of the technique are apparent. We don't think what WE had (have) in mind is unethical because the user would still have to have the locked disk to run the enhancements provided by our 68008 board. But the same technique can obviously be used to unlock various rock-shooting games.
We need not worry about informing you of this technique because the Oct 11 issue of INFOWORLD carried not one but TWO advertisements of products which are specifically designed to 'unlock' locked code via DMA. They have gone one step further in that the devices save the code directly back onto unlocked disk in DOS 3.3 format. So no second processor is needed. (We have LOTS of processors; the use of two processors is not disadvantageous to us!)
Page 8, Column 2
Please understand that we are talking about hardware devices which plug into one of the Apple's I/O slots, NOT just a software program. The first ad was a quarter-pager on p. 28 for "CRACK-SHOT, The Ultimate in Copy De-protection." The ad goes on to state that it even "...cracks all bit copiers in fifteen seconds." Now, THERE is poetic justice. CRACK-SHOT will even unlock those locked 'unlocking' disks!!!
The other ad occupies ALL, would you believe, of page 47. This one is WILDCARD. After carefully explaining that WILDCARD will un-protect ALL repeat ALL 'locked' (6502 variety) software, the advert concludes with the admonishment that you are to use this ONLY for the completely legal purpose of providing archival and backup copies of your locked software. "...and you are not permitted to utilize it for any other use, other than that specified." Hmmm...
We will either develop our own technique or else buy one of these two devices for our own use (one is $150 and the other $130). The fact is that as a businessman your FNE definitely does NOT like not having a backup copy of important software for which we have paid. Sending off the defunct disk (with a usually negligible fee) and hoping for fast turn-around and hoping that the producers of the software have not gone out of business does NOT appeal to us. We want a back-up copy right there where we can get our hands on it, NOW!
In our opinion, this is an ethical viewpoint. There is absolutely no questioning the fact that, under the new copyright law, it is LEGAL. Regrettably, what is ethical is not always congruent with what is legal.
We can be certain that the suppliers of that locked software will disagree with us.
We can also be certain that the presence of those two hardware products are going to move the 'locked disk' war (Apple section) to the next higher level. Let's face it, many Apple user groups exist only to distribute ripped-off software. Any user group can pass the hat and come up with $130-$150. Makes us glad we made the decision to go with unlocked demo software.
REMEMBER THE 'OSBORNE ONE'? That's the computer which, for $1795, you get (as we recall) the computer plus $1800 worth of free software.
Page 9, Column 1
DO NOT REVEAL THIS SECRET:
(whispered) The Osborne Co. does not really pay $1800 for that software that they give away with the $1795 (retail, not wholesale) computer. If we assume their dealer margins are 25% (they may be more or less) than Osborne wholesales the computer AND the software for about $1350. What Osborne is paying for the software over and above the cost of printing the manuals and copying the disks we don't know, but we would guess it is probably at least $50 but almost certainly not as great as $125. Let's try $80, and assume the repro cost is another $45 for all those packages. (Adam, if these figures are so far off that you get angry, just provide us with the correct figures and we will publish them!)
Assuming our figures are correct, this means the purchaser of an Osborne computer is getting, for $125, software that YOU will have to pay $1800 list for! Since there are lots of places where you can find discounts off the list price of that software we will assume that you are clever and have obtained a 30% discount so you will have paid $1260 plus sales tax.
This means that the software producers (and their distribution chain including but not limited to the retail store) want YOU to pay $1215 ($1260 -$45) above the media cost but they will sell to the Osborne Co. for only $80 over the media cost. Which means that either Adam is stealing them blind or that YOU are being shafted for $1135! If you prefer, you can think that you are being charged 1,419% as such as Adam, after the cost of the media is deducted.
We are not absolutely certain but we think this is what is called a two-tier pricing structure.
Let us break this down a little further. We will assume that one of those software packages provided 'free' with the Osborne One retails for $350 list. Assuming that the software producer's share of the total package is proportionate including the media cost, that producer is accepting $15.56 from Adam after media costs are deducted. Assuming a 50% distribution discount, he gets $175 less media cost of $8.75 or $168.25 above the cost of media.
TRY THIS SCENARIO: Ten impecunious college professors (is there any other kind?) band together to purchase one copy of this software package. They then make nine copies so that each of them can use the software on their ten separate computers. We will suppose further that the software producer not only finds out about this but obtains irrefutable proof, acceptable in court, of the professors' actions. Now what?
Now what? is probably either a lawsuit (we've got to make an example of these rotten thieves) or the threat of a lawsuit and most certainly some foaming-at-the-mouth letters to various editors in the style pioneered by Microsoft's Bill Gates.
Page 9, Column 2
What is the terrible, illegal, unforgivable thing that those ten profs did to the software producer? Each of them paid the producer $16.82 above the cost of the media for his software. That's $1.26 MORE repeat MORE than the producer happily sells the same package to Adam for!
Our legal system unquestionably permits the establishment of two-tier pricing, even when the two tiers are as ridiculously far apart as in this example. That's ONE of the reasons we stated earlier that 'legal' and 'ethical' AIN'T congruent!
Some of the problems those software producers are having is a direct result of their ridiculous, irrational, greedy (and in our opinion unethical) pricing posture.
You don't like the figures we used? Plug in your own. You will come to the same conclusion we did.
You think the problem is limited to the few software suppliers dealing with Osborne? No, others such as NLS (and their KAYCOMP) and Morrow Designs are making essentially identical deals with other software vendors.
Look, we believe in the free enterprise system. Let those software vendors set whatever price they like and live with the resulting sales figures. But DO NOT sell a package to someone else for $15.56 and then offer it to US for $350. We are likely to get (you know what!). SURE IT'S LEGAL! But it is unethical as hell.
A company called J.R.T. wrote a CP/M based PASCAL and offered it for sale at $300. A few months later they had sold maybe two or three dozen copies, whoopee. So they (disgustedly?) offered the package for $29.95. Presto! They had about 40,000 sales almost immediately, and they are apparently continuing to sell well because you see full page ads in BYTE and INFOWORLD for that package. Subtract $8.00 media cost from 30 bucks, multiply times 100K+ and subtract 30-50K advertising costs, pay the rent and the front line troops and what do you have left? You figure it out.
For 30 bucks the package can't be any good, right? According to a professional systems-level programmer, it is a very good and very well documented packages and the best CP/M PASCAL available for short programs!
NOT INCIDENTALLY:
We at Digital Acoustics have taken no little amount of flak, especially from retailers, over our 'one price to all' policy for our DTACK GROUNDED line of products.
And we trust that all of our readers are aware of the per copy cost of publishing 10,000 manuals versus making one copy of a disk on demand.
Page 10, Column 1
MORE iAPX 286 STUFF:
Back in newsletter #10, we briefly discussed the impending iAPX 286, hereafter called the 286. That was a prediction not a report because there was relatively little information available at that time. We can now present a report.
AVAILABILITY: Some working parts now exist and in fact working circuit boards also exist; our local Intel representative states that some companies, specifically including Microsoft, have a board. We believe that. However, the status is currently that of 'limited sampling'. That means Microsoft can get one, General Dynamics can get one, but Digital Acoustics will have to wait for awhile.
When new processors are in the limited sampling stage, they often have a few minor glitches. This is normal; the Z8000, 68000 and 8087 all had glitches during this phase. One reason for 'limited sampling' status aside from an actual shortage of wafers is that companies naturally do not like to publicize these problems.
As we recall, the 68000 reached 'limited sampling status' around Feb '80, so the 286 is about 20 months behind the 68000 at this stage. The 68000 in turn was about two years behind the 8086.
PRICING: The 286 is a VERY large chip. According to sources at a competitor, they can only get 40 die on a 4 inch wafer, and at that die size the yield will only be one or two good parts per wafer. And that means that the price will be high.
On the other hand, Intel is now asserting a price of $237, quantity 100. We caution that Intel's prices are not cast in concrete (whose ARE, in this industry?). 8087 prices, predicted and real, have gyrated wildly.
ARCHITECTURE: We had thought that Intel would have added new registers or extended the length of the existing 8086 registers but they did none of the above. In fact, the 286 can best be described as a very modern and high performance memory management chip which, almost as an afterthought, happens to have in on-board microprocessor.
As a result the 286 is spectacularly superior to the 68000 in certain specific areas and spectacularly inferior in others. If you think this means that it is difficult to directly compare the performance of the two units you are wrong. The fact is, it is IMPOSSIBLE to directly compare the two units!
Page 10, Column 2
MEMORY MANAGEMENT AND PROTECTION: The 286 has more sophisticated memory management and protection than any microprocessor (by far) and, we think, than any extant 16 bit minicomputer. For instance, the 68000 has two levels, supervisor and user. The old PDP 11/45 had/has three levels, the highest called the 'kernal'. The 286 his FOUR levels, we kid you not. You will have to get a top secret security clearance before performing a register-to-register add.
The four levels are called 'kernal', 'system services', 'custom extensions' and 'applications'. In addition to these vertical levels of protection, there is also HORIZONTAL protection between tasks! Yes, this is absolutely an ideal multi-tasking system which can use its memory management unit to isolate each user into his or her own segment. THAT SEGMENT MUST BE 64K BYTES OR SMALLER!
ADDRESSING: You will find this hard to believe but with a chip with very nearly DOUBLE the number of devices as the 68000, the maximum linearly addressable memory is 64K bytes. This is for a high performance chip appearing commercially at the SAME time as 256K X 1 dynamic RAMS. Which means the minimum memory size that can be built using one row of sixteen each DRAMs is 1/2 megabyte. Which means the 286 can address that much memory only by using at least EIGHT different segments.
You should also keep in mind that 1 meg DRAMs will appear in about 2 1/2 years, at which time full production shipments of computers using the 286 will just be beginning. The minimum size memory that can be built for the 286 using 1 meg X 1 DRAMs is 16 megabytes, just enough to assign 256 users to his/her own 64K segment. The 286 is fast but it is NOT fast enough for 256 users!
We think restricting the 286 to 64K linearly addressable memory is a mistake, but then what do WE know? Besides, it was probably something that was forced on Intel to maintain downward compatibility with the 8086 and the 8080.
PROMOTION: Intel has begun an advertising campaign which asserts that the 286 is a whole bunch faster than an 8MHz 68000 with memory management. That happens to be true. Let us make an analogy:
Suppose that you are in the market for a motor vehicle. Which should you buy, a Porsche or a stake-bed truck? If you are having troubles making a decision between the two then you have REAL TROUBLES, and we do not mean selecting-a-vehicle type trouble.
If you need to transport 32 sheep from a railroad siding to a lamb chop and mutton factory, you will definitely want to use the stake-bed truck. If you want to transport a friendly-inclined personage of in opposing gender to your pad, surely the Porsche is more appropriate.
Page 11, Column 1
The Porsche is, of course, no other than our old friend the 60000. It is ideal as a spiffy high performance CPU with a huge memory space for one user. The stake-bed truck is the 286, which is ideally suited to accommodate 32 sheep, providing up to 64K RAM for each critter.
WE WERE TELLING THE TRUTH when we said that it was impossible to compare the two devices directly. Instead it should be immediately obvious to the most casual observer that one or the other is best suited to the task at hand. If you prefer the 286 we have this one little question:
Are you going to drive the truck or ride in the back?
While it is impossible to accurately compare the 286 and the 68000, it IS possible to compare them in a SPECIFIC application. In fact, this is exactly what Intel is doing in their adverts - comparing them in a multi-user multi-tasking memory managed and protected environment. Surely you do not expect Intel to publish ads in which the 68000 wins?
So let us compare those two devices in a very simple single-user single-tasking environment such as that favored by us. (Again, such a comparison is unfair to Intel because they did not design the 286 for such an application.) Even in such a clearly-defined circumstance it is difficult to compare the two devices. Consider the following:
- The 286 is vastly superior to the 68000 in string handling within a small memory space. Small means under 64K. The reason is that the 286 has microprogrammed string instructions and the 68000 does not, at least not now. Space HAS been reserved in the instruction set of the 60000 for microprogrammed string instructions, but who knows when they will be implemented?
- The 286 is significantly faster than the 68000 when performing a 16 bit register to register add.
- The 60000 is significantly faster than the 286 when performing a 32 bit register to register add.
- The 60000 is vastly superior to the 286 when working with 32 bit (or
longer) data in a large memory space. Large means over 64K.
Review the data above and tell us which is the better part for our simple application. WE can't decide, assuming the decision is to be made on performance alone. As it happens, there are other factors to consider:
Page 11, Column 2
- Nobody who has worked with a microprocessor such as the 68000 (or the 16032) with a large directly addressable memory will ever willingly get trapped into 64K segments again. The personal computer users who switch to the 286 will come from the ranks of the 8080, Z80, 8085, 8088 users.
- Nobody who has been using the various '80' machines and therefore HAS A SUBSTANTIAL BASE OF USEFUL ASSEMBLY CODE ROUTINES will ever switch to a non-software compatible machine such as the 68000. Besides, these people are accustomed to bank switching. It is a fundamental law of nature that one must segment switch to obtain access to a large memory space, no?
- Nobody who has ever programmed a nice clean machine like the PDP 11 series or the 68000 will ever willingly switch to the convoluted and obscure programming methods needed in the '80' world. Even experienced 6502 users will find a natural affinity with the 68000, even though the 6502 is such less 'natural' to program.
- We therefore conclude that no one who is presently in the '80' camp will select the 68000 over the 286, and vice versa. It's the old Apple-Radio Shack story all over again: Those are two separate worlds and never the twain shall meet. And please do not point out that the Tandy 16 uses a 68000, it does not either USE the 68000!
An idle thought: we wonder who would be stupid enough to take a processor selling in the $200-$400 range (like the 286) and sell it into a simplistic application such as a simple attached processor for the IBM PC?
WHEN IS AN EXTENSION A RETRACTION? When we have the 80287, which is an 'extension' of the 8087 for use with the 286. You see, the 8087 has its own addressing modes, including memory direct. It is necessary to restrict the addressing modes of the 80287 to those which are filtered through the 286s' memory management scheme. Which means the 80287 is an 8087 with some addressing modes deleted. Which means it is a retraction, NOT in extension. Just thought you'd like to know.
IF WE WERE NICE PEOPLE, we wouldn't write what follows: although we have agreed up to now that the 68000 is also an appropriate vehicle for enormously complex systems as well as simple systems such as the ones we favor, it may be time to back away from that agreement. National has actually begun to ship 16032s (our local National distributor has moved "at least four" over the counter to real customers) and limited samples of the 286 exist AND samples of the 68010 either exist or are about to. And all three of those are better computing engines for enormously complex systems than the 60000.
Page 12, Column 1
The reason they are better is the built-in multi-tasking 'hooks' that are missing in the 68000. At least one of them, the 68010, is actually FASTER slightly) than the 68000. And the 286 is faster in some applications.
BUT: the 68000 is beginning to look like what we have been calling it all along: the logical successor to the 6502 as the new generations' fastest and cleanest, as in cleanness of programming, personal microprocessor. Personal as in single-user single-tasker. AND YET: Motorola continues to sandbag and promote the 68000 for complex stuff only. Sigh.
Either Motorola is awfully stupid or we are wrong in our viewpoint (and hence awfully stupid). Since Motorola has hordes of very smart technical types obviously we must be the ones who are wrong, right?
WE HAD PLANNED to publish a list of all the companies offering computers which meet the following three criteria:
- Have a 68000 as the main computing element.
- EITHER support real Bell Labs UNIX, and have a 10 meg or larger disk
to prove it,
OR support a genuine UNIX look-alike which runs on an 87K floppy but is, no lie, almost completely compatible with Unix.
- Are not meeting their sales projections for some unknown reason.
HOWEVER, we decided not to print the list since the press run would bankrupt us. Instead, we are publishing our matrix routine, which now works, along with the 6502 utility code and the Applesoft program listing AND the complete source code of the double precision floating point package. All 62 bits of it.
(About fifteen months ago we were urged, by two different Motorola types, not to give away our floating point package or sell it ridiculously cheaply. Instead we should sell it for $750 to $1500. We were informed that the 68000 was really a minicomputer and that 68000 software should be sold for minicomputer prices.)
(That attitude has resulted in the present lack of software for the 100 or so different brands of 68000 desktop computers.)
Page 12, Column 2
THOSE TOSHIBA RAMS AREN'T AS RELIABLE AS WE THOUGHT! Our new memory test has actually found a few bad 2016s. It looks as if the failure rate is about 1 in 1000, so if you have a 92K DTACK board, there is about one chance in 20 that you have a bad RAM chip. And to think that the motivation for writing that new, better memory test was to check 'bit pattern sensitivity' in our forthcoming dynamic RAM board!
The nice thing about static RAM is that when it is good it stays good and when it is bad it stays bad. Be sure to run your memory test at the highest operating temperature the RAMs are likely to encounter. Which means toward the END of a working day, not at the start.
THE PROJECTED DELIVERY of the dynamic RAM board is about FEB 1 so it will naturally be a couple of months later. Remember, this is our FIRST dynamic RAM product, so development will not be as simple as our other boards. Besides, we want to do everything we can to assure that it is compatible with the new 256K DRAMs.
If we do manage that compatibility, we will have a very nice 2 1/2 megabyte printer buffer on one board,
LATE NEWS FLASHES:
HEWLETT PACKARD has just shot down LISA. The new 68000-based Series 200 model 16 costs $3650 less disk drives. That is less than half LISA's price. For $3650 you get an 80 X 25 CRT display which also supports 400 X 300 HIRES graphics, 128K RAM (expandable to 768K) and a detachable keyboard. For another $1775 they will throw in a dual 3.5 inch floppy, 270K per disk. The disk rotates it 600 RPM, double the usual floppy rate. We will probably buy one to play with.
BY THE WAY, when we arrived at work on 9 Nov, there were two NEC 7220 graphics controller chips on our desk. At $120 each, we obviously purchased them for use as paper weights. For those of you not in the know, the 7220 can draw lines, arcs and circles at 800 nanoseconds per pixel. And it directly supports a 1024 X 1024 display with up to 4 bit planes.
THE FOLLOWING TRADEMARKS ARE ACKNOWLEDGED: Apple, II and soft: Apple Computer Co. Pet: Commodore Business Machines. DTACK GROUNDED and HALGOL: Digital Acoustics, Inc.
SUBSCRIPTIONS: You can subscribe by sending $15/6 issues U.S. and CANADA or $25/6 issues elsewhere. Tell us which issue number to begin with. Make the check out to DTACK GROUNDED. The address is:
DTACK GROUNDED
1415 E. McFadden, Ste, F
SANTA ANA CA 92705
Page 13, Column 1
IN THIS MONTH'S UNCOPYABLE REDLANDS we have (in reverse order) a 62 bit floating point package that works, a matrix inversion routine in 60000 assembly language that works, the 6502 machine code that transfers the array to the 68000 and then fetches the inverted array back AND a sample (and very simple) Applesoft program which can utilize the code.
There are some things which should never be done for the first time, such as riding a bicycle, writing a floating point package, a transcendental package or (and here we get relevant to this issue) a matrix inversion program. The matrix inversion printed here is our FIRST. Any criticism will be both unkind and valid. We didn't even do any 'pivot point' nonsense. In our defense, we will point out that we wrote for advice to two of our subscribers who know more about this stuff than we do, but we have not yet heard from either Ted or Charles.
IN THE MEANTIME, we sent out a half-dozen floppies as soon as we had the program essentially working. We mailed them on 5 Nov and received feedback from two sources within two working days. Bill J. reported that a very well conditioned 77 X 77 matrix was inverted on his 8MHz Dtack board in 50 seconds. That is equivalent to 70 sec for a 100 X 100 matrix using a 12.5MHz Dtack board. His test matrix was the 'minimum of I,J'. That is, A(3,7) = 3 and A(51,14) = 14.
Bob P. reports that a 40 X 40 matrix of random numbers inverted in 3 minutes 9 seconds using Ampersoft and in 10 seconds on his 12.5MHz Dtack board. That is equivalent to 156 seconds for a 100 X 100 matrix.
Page 13, Column 2
The reason Bill's matrix inverted twice as fast as Bob's is that the 'very well conditioned' numbers he used feature mantissas with lots of zeros, and that runs such faster than a matrix featuring random data and therefore random bit patterns in the mantissa.
And the reason for equating to a 100 X 100 matrix is that it requires one million multiplies and one million additions to invert that size matrix. Therefore, a 156 second inversion time means that it takes the 68000 156 microseconds to perform one addition and one multiplication plus the required data movement. And that is a VERY interesting number since it takes the Intel 8087 about 90 microseconds to perform the same two operations, 27 microseconds of which is the time required to load three numbers and 20 of which is the time required to store the result. This means the 8087 is faster than the 68000, right?
WRONG AGAIN, GUYS! To perform a matrix inversion using the 8087, one needs TWO processors, one of which is an 8086 or 8088. And these two processors will set you back several hundred dollars. Therefore they should be fairly compared to TWO 12.5MHz 68000s!! And those two 12.5MHz 68000s can run almost exactly twice as fast as one when performing matrix inversions. So it requires the 8086 and 8087 90 microseconds to perform the same number-crunching task that the 68000 and the 68000 can perform in about 79 microseconds.
(We will now sit back and wait for an indignant letter pointing out that the 8087 calculates using a 52 bit mantissa while OUR double-precision floating point package uses a mere 48 bit mantissa.)
Oh, yes: a 92K Dtack board is big enough to invert a 100 X 100 matrix with double precision (8 byte per number) format. And two 12.5MHz 68000s cost less than an 808X/8087 combo.
Code Listing 1
100 HOME : TEXT :P = 38383:Q = P - 102 110 PRINT CHR$ (4);"BLOADUTILXM,A$7F00" 120 INPUT "INPUT N (SIZE OF MATRIX) ";N 130 DIM A(N - 1,N - 1): REM N X N MATRIX 140 FOR I = 0 TO N - 1: FOR J = 0 TO N - I 150 PRINT "INPUT DATUM FOR ROW ";I + 1;" COL ";J + 1 160 INPUT " "; X 170 A(J,I) = X: NEXT J: NEXT I 180 CALL P: CALL P - 3 190 CALL Q: REM 07 002000 7F00 0700 200 CALL Q: REM 02 002000 210 CALL P - 12 220 PRINT "HERE IS ITS' INVERSE:" 230 PRINT : FOR I = 0 TO N - 1: FOR J = 0 TO N - 1 240 PRINT A(J,I),: NEXT J: PRINT : PRINT : NEXT I 250 END
Code Listing 2
943F 00001 ORG $943F
00002 ;
005E 00003 UPA EQU $5E
0060 00004 UPB EQU $60
006B 00005 SOA EQU $6B
009B 00006 UPC EQU $9B
91AA 00007 SUB05 EQU $91AA
C0A0 00008 RDDATA EQU $C0A0
C0A0 00009 WRDATA EQU $C0A0
C0A1 00010 RDSTAT EQU $C0A1
DEC9 00011 SYNERR EQU $DEC9
E8D5 00012 OVFL EQU $E8D5
EAE1 00013 DIVBY0 EQU $EAE1
00014
00015 ; THIS CODE INVERTS THE FIRST ARRAY IN MEMORY
00016 ;
00017 ; FIRST CHECK THAT THE # OF DIMENSIONS = 2
00018 ;
00019 ; THEN SEND THE TWO DIMENSIONS TO THE 68000.
00020 ;
00021 ; IF THE 68000 RETURNS A ZERO, WE HAVE A
00022 ; SQUARE MATRIX, ELSE REPORT A SYNTAX ERROR.
00023 ;
00024 ; IF WE HAVE A SQUARE MATRIX, THE 68000 RETURNS
00025 ; N SQUARED, WHICH IS THE NUMBER OF FIVE BYTE
00026 ; FLOATING POINT NUMBERS WHICH NEED TO BE SENT
00027 ; TO THE 68000.
00028 ;
00029 ; SEND THIS NUMBER OF FP#S AND THEN RECEIVE THEM
00030 ; BACK, CHECKING EACH VARIABLE FOR AN OVERLFOW.
00031 ;
943F A5 6B 00032 MAT LDA SOA ;-- SET THE PTR TO START
9441 85 5E 00033 STA UPA ; OF THE FIRST ARRAY --
9443 A5 6C 00034 LDA SOA+1
9445 85 5F 00035 STA UPA+1
9447 A0 04 00036 LDY #4
9449 B1 5E 00037 LDA (UPA),Y ;GET THE # OF DIMENSIONS
944B C9 02 00038 CMP #2 ;MUST BE TWO
944D F0 03 00039 BEQ DOK ;SKIP IF OK
944F 4C C9 DE 00040 JMP SYNERR
00041 ;
9452 20 E7 94 00042 DOK JSR OUT4 ;SEND THE TWO DIMENSIONS
9455 20 F3 94 00043 JSR GET1 ;RECV 0 IF THE MATRIX IS SQUARE
9458 F0 03 00044 BEQ SQOK ;SKIP IF SQUARE
945A 4C C9 DE 00045 JMP SYNERR
00046 ;
00047 ; GET THE COUNT AND SAVE IT UN UPB AND UPC
00048 ;
945D 20 F3 94 00049 SQOK JSR GET1 ;HIGH ORDER COUNT
9460 85 61 00050 STA UPB+1
9462 85 9C 00051 STA UPC+1
9464 20 F3 94 00052 JSR GET1 ;LOW ORDER COUNT
9467 85 60 00053 STA UPB
9469 85 9B 00054 STA UPC
00055 ;
00056 ; SET POINTER UPA TO THE START OF THE ARRAY
00057 ;
946B 18 00058 CLC ;ADD #9 TO UPA
946C A9 09 00059 LDA #9
946E 65 5E 00060 ADC UPA
9470 85 5E 00061 STA UPA
9472 90 02 00062 BCC NOCY
9474 E6 5F 00063 INC UPA+1
00064 ;
00065 ; NOW WE SEND THE MATRIX TO THE 68000
00066 ;
00067 ; SEND A FIVE BYTE FP# TO THE 68000
00068 ;
9476 A0 00 00069 NOCY LDY #0
9478 B1 5E 00070 SEND5 LDA (UPA),Y ;FETCH A BYTE FROM THE ARRAY
947A 2C A1 C0 00071 SND5A BIT RDSTAT ;-- WAIT UNTIL THE 68000
947D 70 FB 00072 BVS SND5A ; IS READY FOR DATA --
947F 8D A0 C0 00073 STA WRDATA ;SEND THE BYTE TO THE 68000
9482 C8 00074 INY
9483 C0 05 00075 CPY #5 ;IS Y = 5 ?
9485 D0 F1 00076 BNE SEND5 ;LOOP IF Y IS NOT 5
00077 ;
00078 ; ADD #5 TO THE POINTER UPA
00079 ;
9487 18 00080 CLC
9488 98 00081 TYA ;SET ACC = #5
9489 65 5E 00082 ADC UPA
948B 85 5E 00083 STA UPA
948D 90 02 00084 BCC NOCY1
948F E6 5F 00085 INC UPA+1
00086 ;
00087 ; SUBTRACT ONE FROM THE COUNT IN UPC
00088 ;
9491 38 00089 NOCY1 SEC
9492 A5 9B 00090 LDA UPC
9494 E9 01 00091 SBC #1
9496 85 9B 00092 STA UPC
9498 B0 02 00093 BCS CYOK
949A C6 9C 00094 DEC UPC+1
00095 ;
00096 ; TEST FOR ZERO COUNT
00097 ;
949C 05 9C 00098 CYOK ORA UPC+1
949E D0 D6 00099 BNE NOCY ;LOOP IF NOT ZERO
00100 ;
00101 ; SET POINTER UPA TO THE START OF THE ARRAY
00102 ;
94A0 18 00103 CLC
94A1 A5 6B 00104 LDA SOA
94A3 69 09 00105 ADC #9
94A5 85 5E 00106 STA UPA
94A7 A5 6C 00107 LDA SOA+1
94A9 69 00 00108 ADC #0
94AB 85 5F 00109 STA UPA+1
00110 ;
00111 ; NOW WE RECEIVE THE MATRIX BACK FROM THE 68000
00112 ;
94AD AD A1 C0 00113 GETN LDA RDSTAT ;BYTE AVAILABLE?
94B0 10 FB 00114 BPL GETN ;WAIT FOR BYTE
94B2 AD A0 C0 00115 LDA RDDATA ;GET ERROR BYTE
94B5 F0 0A 00116 BEQ NOERR ;O.K. IF ZERO
94B7 C9 01 00117 CMP #1 ;OVERFLOW?
94B9 D0 03 00118 BNE DIVERR ;DIV BY 0 IF NOT
94BB 4C D5 E8 00119 JMP OVFL ;REPORT OVERFLOW
94BE 4C E1 EA 00120 DIVERR JMP DIVBY0 ;REPORT DIV BY 0
00121 ;
94C1 A0 00 00122 NOERR LDY #0
94C3 AD A0 C0 00123 GET5 LDA RDDATA ;FETCH A BYTE
94C6 91 5E 00124 STA (UPA),Y ;STORE IN ARRAY
94C8 C8 00125 INY
94C9 C0 05 00126 CPY #5
94CB D0 F6 00127 BNE GET5 ;LOOP FOR 5 BYTES
00128 ;
00129 ; ADD #5 TO THE POINTER UPA
00130 ;
94CD 18 00131 CLC
94CE 98 00132 TYA ;SET ACC = #5
94CF 65 5E 00133 ADC UPA
94D1 85 5E 00134 STA UPA
94D3 90 02 00135 BCC NOCY2
94D5 E6 5F 00136 INC UPA+1
00137 ;
00138 ; SUBTRACT ONE FROM THE COUNT IN UPB
00139 ;
94D7 38 00140 NOCY2 SEC
94D8 A5 60 00141 LDA UPB
94DA E9 01 00142 SBC #1
94DC 85 60 00143 STA UPB
94DE B0 02 00144 BCS CYOK1
94E0 C6 61 00145 DEC UPB+1
00146 ;
94E2 05 61 00147 CYOK1 ORA UPB+1
94E4 D0 C7 00148 BNE GETN ;LOOP IF COUNT IS NOT ZERO
00149 ;
94E6 60 00150 RTS ;MATRIX INVERSION COMPLETED
00151 ;
00152 ; SEND 1, 2 OR 4 BYTES; FIRST INCREMENTING Y
00153 ;
94E7 20 EA 94 00154 OUT4 JSR OUT2
94EA 20 ED 94 00155 OUT2 JSR OUT1
94ED C8 00156 OUT1 INY ;INCR INDEX Y
94EE B1 5E 00157 LDA (UPA),Y
94F0 4C AA 91 00158 JMP SUB05 ;OUTPUT THE BYTE
00159 ;
00160 ; GET A BYTE FROM THE 68000
00161 ;
94F3 AD A1 C0 00162 GET1 LDA RDSTAT ;BYTE AVAILABLE?
94F6 10 FB 00163 BPL GET1 ;WAIT FOR BYTE
94F8 AD A0 C0 00164 LDA RDDATA ;READ THE INPUT PORT
94FB 60 00165 RTS ;RETURN WITH BYTE
Code Listing 3
1 OPT P=68000,BRS,FRS
2 ; NOTE: SEE BUG FIXES IN DG#17P3,P4;DG#18P32.
3
4 ; ***** MATRIX INVERSION ROUTINE FOR HALGOL *****
5 ;
6 ; COPYRIGHT 1982 DIGITAL ACOUSTICS INC.
7 ;
8 ; THIS PACKAGE INCLUDES A DOUBLE PRECISION
9 ; FLOATING POINT PACKAGE WITH A 48 BIT MANTISSA
10 ;
11 ;
12 ; FOLLOWING ARE I/O ASSIGNMENTS:
13 ;
# 00000FFA 14 STATUS EQU $0FFA
# 00000FF8 15 DATIN EQU $0FF8
# 00000FFA 16 DATOUT EQU $0FFA
17 ;
18 ; FOLLOWING ARE MEMORY ASSIGNMENTS
19 ; USED BY THE BOOTSTRAP ROM (MONITOR):
20 ;
# 00000122 21 IDLE EQU $0122
# 0000109C 22 ADR EQU $109C
# 000010A0 23 NSTAR EQU $10A0
# 000010A2 24 T EQU $10A2
25 ;
26 ; FOLLOWING ARE MEMORY ASSIGNMENTS FOR THIS CODE:
27 ;
# 000018F4 28 R EQU $18F4
# 00001902 29 S1 EQU R+14
# 00001904 30 M1 EQU S1+2
# 0000190A 31 S2 EQU S1+8
# 0000190C 32 M2 EQU S2+2
# 00001912 33 FPT EQU S2+8
# 0000191A 34 FPU EQU FPT+8
# 00001922 35 LOGX EQU FPU+8
# 00001922 36 BCDX EQU LOGX
# 00001922 37 SINSGN EQU LOGX
# 00001924 38 SERCNT EQU LOGX+2
# 00001926 39 EXPADD EQU LOGX+4 ;EXP ADDER
# 0000192F 40 ERRID EQU LOGX+13 ;ERROR ID #
# 00001930 41 ERRPTR EQU LOGX+14 ;ERROR POINTER
# 00001932 42 STR EQU LOGX+16 ;MISC STRING AREA
43 ;
44
002000 45 ORG $2000 ;TEMP FOR DEV
46 ;
002000 4EB8 2112 47 JSR GETN ;GET N, MATRIX
002004 61 08 48 BSR INVMAT ;INVERT MATRIX
002006 4EB8 2206 49 JSR SENDN ;RETN MAT TO HOST
00200A 4EF8 0122 50 JMP IDLE ;RETURN TO BOOT
51 ;
52 ; INVERT A MATRIX BY PERFORMING N FRAMES
53 ;
00200E 11F8 26C7 1926 54 INVMAT MOVE.B N+3,FCTR ;SET UP FRAMT CTR
55 ;
56 ; PERFORM ONE FRAME OF THE INVERSION PROCESS
57 ;
58 ; FIRST WE WILL CALC A(1,1) = 1/A(1,1)
59 ;
002014 3C7C 26D0 60 FLOOP MOVE.W #RPTR,A6 ;PT TO ROW1 PTR
002018 225E 61 MOVE.L (A6)+,A1 ;A2 IS ROW1 PTR
00201A 3478 26CE 62 MOVE.W CPTR,A2 ;A2 PT TO COL1 PTR
00201E 2049 63 MOVE.L A1,A0 ;ROW START ADDR
002020 D1DA 64 ADDA.L (A2)+,A0 ;ADD COL1 OFFSET
65 ;
66 ; A0 POINTS AT ELEMENT 1,1
67 ;
002022 21D8 1902 68 MOVE.L (A0)+,S1 ;A(1,1) TO FPACC1
002026 21D8 1906 69 MOVE.L (A0)+,M1+2
00202A 21FC 10018000 70 MOVE.L #$10018000,S2 ;#1 TO FPACC2
190A
002032 42B8 190E 71 CLR.L M2+2
002036 4EB8 2302 72 JSR LDIV1 ;CALC RECIPROCAL
00203A 2678 1906 73 MOVE.L M1+2,A3
00203E 2878 1902 74 MOVE.L S1,A4 ;RESULT IN A4,A3
002042 210B 75 MOVE.L A3,-(A0)
002044 210C 76 MOVE.L A4,-(A0) ;STORE 1/A(1,1)
77 ;
78 ; FOR I = 2 TO N, A(1,I)=A(1,I) TIMES 1/A(1,1)
79 ;
002046 1038 26C7 80 MOVE.B N+3,D0 ;FETCH N AS BYTE
00204A 5300 81 SUBQ.B #1,D0 ;N - 1
00204C 11C0 1924 82 MOVE.B D0,SERCNT ;SET LOOP COUNT
83 ;
002050 2049 84 ROW1 MOVE.L A1,A0 ;A0 IS ROW START
002052 D1DA 85 ADDA.L (A2)+,A0 ;ADD COL OFFSET
002054 21CC 1902 86 MOVE.L A4,S1 ;1/A(1,1) TO FPACC1
002058 21CB 1906 87 MOVE.L A3,M1+2
00205C 4EB8 2220 88 JSR LMUL ;FPACC1 * (A0)
002060 2138 1906 89 MOVE.L M1+2,-(A0)
002064 2138 1902 90 MOVE.L S1,-(A0) ;STORE RESULT
002068 5338 1924 91 SUBQ.B #1,SERCNT ;DECREMENT COUNT
00206C 66 E2 92 BNE ROW1 ;LOOP UNTIL DONE
93 ;
94
95 ; TO COMPLETE THE FRAME, PERFORM THESE CALCS:
96 ;
97 ; FOR R = 2 TO N: B = -A(R,1): A(R,1)=0
98 ; FOR C = 1 TO N: A(R,C) = A(R,C) + B * A(1,C)
99 ; NEXT C: NEXT R: FRAME IS THEN COMPLETE
100 ;
101 ; A1 IS PTR TO 1ST ROW
102 ; A2 IS PTR TO COL PTR
103 ; A5 IS PTR TO ROW R
104 ; A6 IS PTR TO ROW PTR
105 ; RETAIN B IN A4, A3
106 ;
# 00001922 107 RCTR EQU LOGX
# 00001925 108 CCTR EQU LOGX+3
109 ;
00206E 1038 26C7 110 MOVE.B N+3,D0 ;FETCH N AS BYTE
002072 5300 111 SUBQ.B #1,D0
002074 11C0 1922 112 MOVE.B D0,RCTR ;OUTER LOOP CTR
113 ;
002078 2A5E 114 RLOOP MOVE.L (A6)+,A5 ;A5 IS ROW R PTR
00207A 3478 26CE 115 MOVE.W CPTR,A2 ;A2 IS COL1 PTR
00207E 204D 116 MOVE.L A5,A0
002080 D1D2 117 ADDA.L (A2),A0 ;A0 PTS TO A(R,1)
002082 0850 0007 118 BCHG #7,(A0) ;CHANGE THE SIGN
002086 2850 119 MOVE.L (A0),A4
002088 4298 120 CLR.L (A0)+
00208A 2650 121 MOVE.L (A0),A3 ;B TO A4,A3
00208C 4290 122 CLR.L (A0) ;A(R,1) = 0
123 ;
00208E 11F8 26C7 1925 124 MOVE.B N+3,CCTR ;SET UP COL CTR
002094 2049 125 CLOOP MOVE.L A1,A0 ;A0 PTS TO A(1,1)
002096 D1D2 126 ADDA.L (A2),A0 ;A0 PTS TO A(1,C)
002098 21CC 1902 127 MOVE.L A4,S1
00209C 21CB 1906 128 MOVE.L A3,M1+2 ;B TO FPACC1
0020A0 4EB8 2220 129 JSR LMUL ;CALC B * A(1,C)
130 ;
0020A4 204D 131 MOVE.L A5,A0
0020A6 D1DA 132 ADDA.L (A2)+,A0 ;A0 PTS TO A(R,C)
0020A8 4EB8 23A8 133 JSR LADD ;A(R,C)+B*A(1,C)
134 ;
0020AC 2138 1906 135 MOVE.L M1+2,-(A0)
0020B0 2138 1902 136 MOVE.L S1,-(A0) ;RESULT TO A(R,C)
137 ;
0020B4 5338 1925 138 SUBQ.B #1,CCTR ;DECR COL CTR
0020B8 66 DA 139 BNE CLOOP ;LOOP UNTIL DONE
140 ;
0020BA 5338 1922 141 SUBQ.B #1,RCTR ;DECR ROW CTR
0020BE 66 B8 142 BNE RLOOP ;LOOP UNTIL DONE
143 ;
144 ; NOW ROTATE THE ROW AND COLUMN POINTERS
145 ;
0020C0 61 0A 146 BSR ROTCR ;ROTATE THEM
147 ;
0020C2 5338 1926 148 SUBQ.B #1,FCTR ;DECR FRAME CTR
0020C6 6600 FF4C 149 BNE FLOOP ;LOOP UNTIL DONE
150 ;
0020CA 4E75 151 RTS ;MATRIX INVERTED
152 ;
153
154 ; ROTATE THE COLUMN AND ROW POINTERS
155 ;
0020CC 307C 26D0 156 ROTCR MOVE.W #RPTR,A0 ;POINT A0 AT ROW 0
0020D0 4EB8 20D4 157 JSR ROT ;ROTATE COLUMNS
158 ;
159 ; SUBR' ROT LEAVES A0 POINTING AT COL OFFSET 0.
160 ; NOW WE USE SUBROUTINE ROT A SECOND TIME
161 ; TO ROTATE THE COLUMN OFFSETS.
162 ;
0020D4 1038 26C7 163 ROT MOVE.B N+3,D0 ;GET BYTE VALUE
0020D8 5300 164 SUBQ.B #1,D0 ;D0 = N - 1
0020DA 3248 165 MOVE.W A0,A1
0020DC 2F19 166 MOVE.L (A1)+,-(A7) ;1ST PTR TO STK
167 ;
0020DE 20D9 168 ROT1 MOVE.L (A1)+,(A0)+ ;MOVE 1 PTR
0020E0 5300 169 SUBQ.B #1,D0 ;DECR CTR
0020E2 66 FA 170 BNE ROT1 ;LOOP N-1 TIMES
171 ;
0020E4 20DF 172 MOVE.L (A7)+,(A0)+ ;LAST PTR WAS 1ST
0020E6 4E75 173 RTS
174 ;
175 ; SET UP THE ROW AND COLUMN POINTERS
176 ;
0020E8 2038 26C4 177 SURCP MOVE.L N,D0 ;N AS 32 BIT VALUE
0020EC 2200 178 MOVE.L D0,D1
0020EE E749 179 LSL.W #3,D1 ;D1 = 8 * N
0020F0 307C 26D0 180 MOVE.W #RPTR,A0 ;A0 = ROW PTR START
0020F4 2408 181 MOVE.L A0,D2 ;UPPER WORD IS ZERO
0020F6 D481 182 ADD.L D1,D2 ;D2 = ARRAY START
0020F8 31C2 26CC 183 MOVE.W D2,ARYST ;ST STARTING ADDR
0020FC 61 08 184 BSR STORPT ;STORE ROW PTRS
185 ;
0020FE 31C8 26CE 186 MOVE.W A0,CPTR ;ST COL START ADR
002102 72 08 187 MOVEQ #8,D1 ;SET D1 = 8
002104 4282 188 CLR.L D2 ;SET D2 = 0
189 ;
190 ; EXIT, STORING COL OFFSETS
191 ;
002106 1600 192 STORPT MOVE.B D0,D3 ;COUNT N TO D3
002108 20C2 193 STO1 MOVE.L D2,(A0)+ ;STORE A POINTER
00210A D481 194 ADD.L D1,D2 ;CALC NX PTR
00210C 5303 195 SUBQ.B #1,D3 ;DECR COUNT
00210E 66 F8 196 BNE STO1 ;LOOP UNTIL DONE
002110 4E75 197 RTS ;DONE
198 ;
199
200 ; SUBROUTINE; GET N AND TEST FOR SQUARE MATRIX
201 ;
002112 307C 0FFA 202 GETN MOVE.W #STATUS,A0 ;-- SET UP THE
002116 327C 0FF8 203 MOVE.W #DATIN,A1 ; I/O PARMS --
00211A 7E 07 204 MOVEQ #7,D7
00211C 7C 06 205 MOVEQ #6,D6
00211E 4281 206 CLR.L D1
002120 61 38 207 BSR GET2 ;FETCH N = DIM
002122 21C1 26C4 208 MOVE.L D1,N ;STORE N IN MEM
002126 2401 209 MOVE.L D1,D2
002128 61 30 210 BSR GET2 ;GET 2ND DIM
00212A B441 211 CMP.W D1,D2 ;SQUARE MATRIX?
212
00212C 6600 00AA 213 BNE.W ERR1 ;ERROR IF NOT SQ
214
002130 C2C2 215 MULU D2,D1 ;D1 = # OF VARS
002132 2A01 216 MOVE.L D1,D5 ;SAVE #VAR'S IN D5
002134 21C1 26C8 217 MOVE.L D1,NSQD ;SAVE FOR LATER
218 ;
219 ; RETURN A ZERO ERROR CODE
220 ;
002138 4240 221 CLR.W D0 ;D0 = ZERO
00213A 0D10 222 GETN1 BTST D6,(A0) ;READY FOR BYTE
00213C 66 FC 223 BNE GETN1 ;WAIT TIL RDY
00213E 1080 224 MOVE.B D0,(A0) ;SEND ZERO BYTE
225 ;
226 ; SEND THE NUMBER OF VARIABLES ( = N SQUARED )
227 ;
002140 61 58 228 BSR SEND2 ;# VAR'S TO HOST
002142 4EB8 20E8 229 JSR SURCP ;ROWS & COL'S
002146 307C 0FFA 230 MOVE.W #STATUS,A0 ;RESTORE A0
00214A 3478 26CC 231 MOVE.W ARYST,A2 ;A2 = ARRAY START
00214E 61 18 232 GETN2 BSR GETFP ;GET AN FP#
002150 24C0 233 MOVE.L D0,(A2)+ ;STORE IT
002152 24C1 234 MOVE.L D1,(A2)+ ;( 8 BYTES )
002154 5345 235 SUBQ.W #1,D5 ;DECR VAR COUNT
002156 66 F6 236 BNE GETN2 ;LOOP TIL DONE
002158 4E75 237 RTS
238 ;
239 ; SUBROUTINE; GET TWO BYTES FROM HOST
240 ;
00215A 0F10 241 GET2 BTST D7,(A0) ;BYTE AVAIL?
00215C 67 FC 242 BEQ GET2 ;WAIT FOR BYTE
00215E 3211 243 MOVE.W (A1),D1
002160 0F10 244 GET2A BTST D7,(A0) ;NEXT BYTE RDY?
002162 67 FC 245 BEQ GET2A ;WAIT FOR BYTE
002164 1211 246 MOVE.B (A1),D1
002166 4E75 247 RTS
248 ;
249
250 ; SUBR; ACCEPT A MICROSOFT FORMAT F.P. # FROM THE
251 ; HOST AND EXPAND IT INTO THE 62 BIT F.P. FORMAT
252 ;
002168 0F10 253 GETFP BTST D7,(A0) ;BYTE READY?
00216A 67 FC 254 BEQ GETFP ;WAIT FOR BYTE
00216C 4240 255 CLR.W D0
00216E 1011 256 MOVE.B (A1),D0 ;FETCH THE EXP
002170 67 1E 257 BEQ FPZERO ;SKIP IF ZERO
258 ;
002172 0640 0F80 259 ADDI.W #$0F80,D0 ;CORRECT THE OFFSET
002176 61 E2 260 BSR GET2 ;HIGH 16 MANT BITS
261 ;
262 ; RECOVER SIGN FROM D7 OF HOST MANT
002178 3401 263 MOVE.W D1,D2 ;COPY MANT TO D2
00217A 0241 8000 264 ANDI.W #$8000,D1 ;SIGN IN D1
00217E 8041 265 OR.W D1,D0 ;ADD SIGN TO EXP
002180 0042 8000 266 ORI.W #$8000,D2 ;MANT MSBIT = 1
002184 4840 267 SWAP D0
002186 3002 268 MOVE.W D2,D0 ;32 BITS IN D0
002188 61 D0 269 BSR GET2 ;GET REST OF MANT
00218A 4841 270 SWAP D1
00218C 4241 271 CLR.W D1
00218E 4E75 272 RTS ;FP# IN D0,D1
273 ;
002190 61 C8 274 FPZERO BSR GET2 ;DISCARD 4 BYTES
002192 61 C6 275 BSR GET2
002194 4280 276 CLR.L D0 ;RESULT IS ZERO
002196 4281 277 CLR.L D1
002198 4E75 278 RTS ;FP# IN D0, D1
279 ;
280 ; SUBROUTINE; SEND D1 TO HOST AS TWO BYTE NUMBER
281 ;
00219A 0D10 282 SEND2 BTST D6,(A0) ;HOST RDY FOR BYTE?
00219C 66 FC 283 BNE SEND2 ;WAIT TIL RDY
00219E 3081 284 MOVE.W D1,(A0) ;SEND M.S.BYT
0021A0 0D10 285 SEND2A BTST D6,(A0)
0021A2 66 FC 286 BNE SEND2A
0021A4 1081 287 MOVE.B D1,(A0) ;SEND L.S.BYT
0021A6 4E75 288 RTS
289 ;
290 ; SUBROUTINE; UNPACK 62 BIT F.P. # TO THE HOST'S
291 ; FIVE BYTE FORMAT, REPORTING OVERFLOWS.
292 ;
0021A8 4238 1901 293 XMITFP CLR.B S1-1 ;CLEAR ERROR BYTE
0021AC 4C91 000F 294 MOVEM.W (A1),D0-D3 ;FETCH 8 BYTES
0021B0 5089 295 ADDQ.L #8,A1 ;PTR TO NEXT FP#
296 ;
297 ; ROUND THE 48 BIT MANT TO 32 BITS
298 ;
0021B2 3803 299 MOVE.W D3,D4 ;TEST MSB
0021B4 6A 0A 300 BPL CMPR ;SKIP IF ZERO
0021B6 5242 301 ADDQ.W #1,D2
0021B8 64 06 302 BCC CMPR
0021BA 5241 303 ADDQ.W #1,D1
0021BC 64 02 304 BCC CMPR
0021BE 5240 305 ADDQ.W #1,D0 ;INCR EXP
306 ;
307
308 ; MASK THE SIGN ONTO THE MSB OF THE MANT
309 ;
0021C0 3600 310 CMPR MOVE.W D0,D3
0021C2 0043 7FFF 311 ORI.W #$7FFF,D3 ;D3 = 7FFF OR FFFF
0021C6 C243 312 AND.W D3,D1 ;SIGN TO MANT MSB
0021C8 0240 7FFF 313 ANDI.W #$7FFF,D0 ;ZERO THE SIGN
314 ;
0021CC 0440 0F80 315 SUBI.W #$0F80,D0 ;CORRECT OFFSET
0021D0 6B 2C 316 BMI RZERO ;ZERO ON UNDFL
0021D2 0C40 0100 317 CMPI.W #256,D0 ;OVERFLOW
0021D6 65 12 318 BCS CMPR0 ;SKIP IF O.K.
319 ;
0021D8 7E 01 320 ERR1 MOVEQ #1,D7
0021DA 0838 0006 0FFA 321 ERROR BTST #6,STATUS ;HOST RDY?
0021E0 66 F8 322 BNE ERROR ;WAIT TIL RDY
0021E2 11C7 0FFA 323 MOVE.B D7,DATOUT ;SEND ERR I.D.
0021E6 4EF8 0122 324 JMP IDLE ;RETURN TO BOOT
325 ;
326 ; FIRST SEND THE ERROR BYTE
327 ;
0021EA 0D10 328 CMPR0 BTST D6,(A0) ;HOST RDY FOR BYT?
0021EC 66 FC 329 BNE CMPR0 ;WAIT TIL RDY
0021EE 10B8 1901 330 MOVE.B S1-1,(A0) ;SEND ERR CODE
331 ;
332 ; NOW SEND THE FLOATING POINT NUMBER, 5 BYTES
333 ;
0021F2 0D10 334 CMPR1 BTST D6,(A0) ;HOST RDY FOR BYTE?
0021F4 66 FC 335 BNE CMPR1 ;WAIT TIL RDY
0021F6 1080 336 MOVE.B D0,(A0) ;SEND EXP
337 ;
0021F8 61 A0 338 BSR SEND2 ;SEND D1
0021FA 3202 339 MOVE.W D2,D1
0021FC 60 9C 340 BRA SEND2 ;EXIT, SEND'G 2
341 ;
0021FE 4240 342 RZERO CLR.W D0 ;RESULT IS ZERO
002200 4241 343 CLR.W D1
002202 4242 344 CLR.W D2
002204 60 E4 345 BRA CMPR0 ;SEND THE ZERO
346 ;
347 ; SEND THE INVERTED MATRIX BACK TO THE HOST
348 ;
002206 307C 0FFA 349 SENDN MOVE.W #STATUS,A0
00220A 7C 06 350 MOVEQ #6,D6
00220C 3278 26CC 351 MOVE.W ARYST,A1
002210 2A38 26C8 352 MOVE.L NSQD,D5 ;SET VAR COUNT
353 ;
002214 61 92 354 SENDN2 BSR XMITFP ;5 BYTE FP#
002216 5345 355 SUBQ.W #1,D5 ;DECR VAR CNT
002218 66 FA 356 BNE SENDN2 ;LOOP TIL DONE
00221A 4E75 357 RTS ;DONE
358 ;
359
360 ; STORE A ZERO IN FPACC1
361 ;
00221C 4EF8 22F0 362 RZER JMP RZER1
363 ;
364 ; FETCH AN 8 BYTE F.P. NUMBER TO FPACC#2
365 ;
002220 21D8 190A 366 LMUL MOVE.L (A0)+,S2
002224 21D8 190E 367 MOVE.L (A0)+,M2+2
368 ;
369 ; PERFORM A 62 BIT FLOATING POINT MULTIPLY
370 ;
002228 4CB8 00FF 1902 371 LMUL1 MOVEM.W S1,D0-D7 ;FETCH BOTH #S
00222E 3F00 372 MOVE.W D0,-(A7) ;PUSH S1
002230 B940 373 EOR D4,D0
002232 0240 8000 374 ANDI.W #$8000,D0
002236 31C0 1902 375 MOVE.W D0,S1 ;STORE THE SIGN
00223A 301F 376 MOVE.W (A7)+,D0 ;RESTORE X1
00223C E348 377 LSL.W #1,D0 ;TEST FOR ZERO
00223E 67 DC 378 BEQ RZER ;EXIT IF FPACC1 0
002240 E34C 379 LSL.W #1,D4 ;TEST FOR ZERO
002242 67 D8 380 BEQ RZER ;EXIT IF FPACC2 0
002244 D044 381 ADD.W D4,D0 ;ADD EXPONENTS
002246 E248 382 LSR.W #1,D0 ;CORRECT FOR SHIFT
002248 0440 1000 383 SUBI.W #$1000,D0 ;CORRECT OFFSET
00224C 6B CE 384 BMI RZER ;ZERO IF
00224E 3F00 385 MOVE.W D0,-(A7) ;PUSH EXP
002250 3003 386 MOVE.W D3,D0 ;USE D0 AS SCRATCH
002252 C0C7 387 MULU D7,D0 ;A0 * B0
002254 4240 388 CLR.W D0 ;DISCARD LOWER 16
002256 4840 389 SWAP D0 ;D0 = $0000HHHH
002258 4244 390 CLR.W D4 ;D4 IS SCRATCH
00225A 3202 391 MOVE.W D2,D1 ;DESTROYS A2
00225C C2C7 392 MULU D7,D1 ;A1 * B0
00225E D081 393 ADD.L D1,D0 ;SUM PARTIALS
002260 64 02 394 BCC LMUL2 ;SKIP IF NO CY
002262 5204 395 ADDQ.B #1,D4 ;ACCUM CYS IN D4
002264 3203 396 LMUL2 MOVE.W D3,D1
002266 C2C6 397 MULU D6,D1 ;A0 * B1
002268 D081 398 ADD.L D1,D0 ;SUM PARTIALS
00226A 64 02 399 BCC LMUL3 ;SKIP IF NO CY
00226C 5204 400 ADDQ.B #1,D4 ;ACCUM CYS IN D4
401 ;
402 ; THE NEXT TWO INSTRUCTIONS CLEVERLY DISCARDS
403 ; THE LOWER 16 BITS WHILE MOVING THE CARRIES
404 ; FROM D4 INTO THEIR PROPER POSITION
405 ;
00226E 3004 406 LMUL3 MOVE.W D4,D0
002270 4840 407 SWAP D0
408 ;
002272 4244 409 CLR.W D4 ;CLR FOR MORE CY'S
002274 C6C5 410 MULU D5,D3 ;B2 * A0
411 ;
412
413 ; D3 IS NOW AVAILABLE AS SCRATCH REGISTER
414 ;
002276 D083 415 ADD.L D3,D0 ;ADD PARTIALS
002278 64 02 416 BCC LMUL4 ;SKIP IF NO CY
00227A 5204 417 ADDQ.B #1,D4
00227C 3202 418 LMUL4 MOVE.W D2,D1
00227E C2C6 419 MULU D6,D1 ;B1 * A1
002280 D081 420 ADD.L D1,D0
002282 64 02 421 BCC LMUL5
002284 5204 422 ADDQ.B #1,D4
002286 3638 1904 423 LMUL5 MOVE.W M1,D3 ;A2 IS IN D3
00228A CEC3 424 MULU D3,D7 ;A2 * B0
00228C D087 425 ADD.L D7,D0
426 ;
427 ; D7 IS NOW AVAILABLE AS A SCRATCH REGISTER
428 ;
00228E 64 02 429 BCC LMUL6
002290 5204 430 ADDQ.B #1,D4
002292 3E00 431 LMUL6 MOVE.W D0,D7 ;SAVE GUARD WORD
432 ;
433 ; GET CLEVER AGAIN
434 ;
002294 3004 435 MOVE.W D4,D0
002296 4840 436 SWAP D0
002298 4244 437 CLR.W D4 ;READY FOR CY'S
00229A 3203 438 MOVE.W D3,D1
00229C C2C6 439 MULU D6,D1 ;B1 * A2
00229E D081 440 ADD.L D1,D0
0022A0 64 02 441 BCC LMUL7
0022A2 5204 442 ADDQ.B #1,D4
0022A4 C4C5 443 LMUL7 MULU D5,D2 ;B2 * A1
0022A6 D082 444 ADD.L D2,D0
445 ;
446 ; D2 IS NOW AVAILABLE AS SCRATCH REGISTER
447 ;
0022A8 64 02 448 BCC LMUL8
0022AA 5204 449 ADDQ.B #1,D4
0022AC 3400 450 LMUL8 MOVE.W D0,D2 ;SAVE 16 BITS
0022AE 3004 451 MOVE.W D4,D0
0022B0 4840 452 SWAP D0 ;SLIGHTLY CLEVER
0022B2 321F 453 MOVE.W (A7)+,D1 ;POP EXP TO D1
0022B4 C6C5 454 MULU D5,D3 ;B2 * A2
0022B6 D083 455 ADD.L D3,D0 ;NO CY POSSIBLE
0022B8 6B 0C 456 BMI LMUL9 ;SKIP IF B31 = 1
0022BA E34F 457 LSL.W #1,D7
0022BC E352 458 ROXL.W #1,D2
0022BE E390 459 ROXL.L #1,D0 ;SHIFT RESULT L 1
460 ;
461 ; NEXT BRANCH TAKEN ONLY IF MANTS IMPROPER
462 ;
0022C0 6A 2E 463 BPL RZER1
0022C2 5341 464 SUBQ.W #1,D1 ;DECR EXP BY 1
0022C4 6B 2A 465 BMI RZER1 ;ZERO IF UNDFL
466 ;
467
468 ; ROUND THE RESULT
469 ;
0022C6 E34F 470 LMUL9 LSL.W #1,D7 ;SHIFT GUARD
0022C8 64 0A 471 BCC LMUL10 ;DONE IF B-1 IS 0
0022CA 5242 472 ADDQ.W #1,D2 ;ELSE ROUND UP
0022CC 64 06 473 BCC LMUL10 ;SKIP IF NO CY
0022CE 5280 474 ADDQ.L #1,D0 ;ADD CY TO D0
0022D0 64 02 475 BCC LMUL10 ;SKIP I NO OVFL
0022D2 5241 476 ADDQ.W #1,D1 ;INCREMENT EXP
477 ;
0022D4 3601 478 LMUL10 MOVE.W D1,D3 ;SET FLAGS
0022D6 67 18 479 BEQ RZER1 ;ZERO IF EXP 0
0022D8 0243 6000 480 ANDI.W #$6000,D3 ;TEST EXP OVFL
0022DC 66 0E 481 BNE OVFL ;REPORT OVERFLOW
482 ;
483 ; MULTIPLICATION IS COMPLETE, STORE THE RESULT
484 ;
0022DE 8378 1902 485 OR D1,S1 ;STORE EXP
0022E2 21C0 1904 486 MOVE.L D0,M1
0022E6 31C2 1908 487 MOVE.W D2,M1+4 ;STORE MANTISSA
0022EA 4E75 488 RTS
489 ;
490 ; THE FLOATING POINT MULTIPLY ROUTINE IS COMPLETED
491 ;
0022EC 4EF8 21D8 492 OVFL JMP ERR1 ;REPORT OVERFLOW
493 ;
494
495 ; STORE A ZERO IN FPACC1
496 ;
0022F0 42B8 1902 497 RZER1 CLR.L S1
0022F4 42B8 1906 498 CLR.L M1+2
0022F8 4E75 499 RTS
500 ;
501 ; FETCH AN 8 BYTE F.P. NUMBER TO FPACC#2
502 ;
0022FA 21D8 190A 503 LDIV MOVE.L (A0)+,S2
0022FE 21D8 190E 504 MOVE.L (A0)+,M2+2
505 ;
506 ; PERFORM A 62 BIT FLOATING POINT DIVIDE
507 ;
002302 4CB8 00FF 1902 508 LDIV1 MOVEM.W S1,D0-D7 ;FETCH BOTH #S
002308 3F00 509 MOVE.W D0,-(A7) ;PUSH S1
00230A B940 510 EOR.W D4,D0
00230C 0240 8000 511 ANDI.W #$8000,D0
002310 31C0 1902 512 MOVE.W D0,S1 ;STORE THE SIGN
002314 301F 513 MOVE.W (A7)+,D0 ;RESTORE X2
002316 E348 514 LSL.W #1,D0 ;TEST FOR ZERO
002318 67 76 515 BEQ DIV0 ;ERR IF FPACC1 0
00231A E34C 516 LSL.W #1,D4 ;TEST FOR ZERO
00231C 67 D2 517 BEQ RZER1 ;EXIT IF FPACC2 0
00231E 9840 518 SUB.W D0,D4 ;SUB EXPONENTS
002320 E244 519 ASR.W #1,D4 ;CORRECT FOR SHIFT
002322 0644 1000 520 ADDI.W #$1000,D4 ;CORRECT OFFSET
521 ;
522 ; DO NOT TEST FOR OVERFLOW OR UNDERFLOW YET
523 ;
002326 4841 524 SWAP D1
002328 3202 525 MOVE.W D2,D1 ;M1 IN D1.L, D3.W
00232A 4845 526 SWAP D5
00232C 3A06 527 MOVE.W D6,D5 ;M2 IN D5.L, D7.W
00232E 4282 528 CLR.L D2
002330 7C 32 529 MOVEQ #50,D6 ;SET FOR 50 LOOPS
002332 60 06 530 BRA LDIV3
531 ;
532 ; SHIFT THE NUMERATOR 1 BIT LEFT
533 ;
002334 E34F 534 LDIV2 LSL.W #1,D7
002336 E395 535 ROXL.L #1,D5
002338 65 0C 536 BCS SUBDO ;SUB IF CY = 1
537 ;
00233A B285 538 LDIV3 CMP.L D5,D1 ;COMPARE HIGH ORDER
00233C 65 08 539 BCS SUBDO
00233E 66 0C 540 BNE NOSUB
541 ;
002340 B647 542 CMP.W D7,D3 ;COMPARE LOW ORDER
002342 65 02 543 BCS SUBDO
002344 66 06 544 BNE NOSUB
545 ;
002346 9E43 546 SUBDO SUB.W D3,D7
002348 9B81 547 SUBX.L D1,D5
00234A 5202 548 ADDQ.B #1,D2 ;BIT 1 TO D2,B0
549 ;
550
551 ; SHIFT A 1 OR ZERO INTO THE RESULT
552 ;
00234C E38A 553 NOSUB LSL.L #1,D2
00234E E390 554 ROXL.L #1,D0 ;64 BIT SHIFT L
555 ;
002350 5306 556 SUBQ.B #1,D6
002352 66 E0 557 BNE LDIV2 ;LOOP UNTIL ZERO
558 ;
559 ; TEST WHETHER THE MSB IS 1. IF SO, SHIFT THE
560 ; RESULT 1 BIT RIGHT AND ADD #1 TO EXP
561 ;
002354 0800 0012 562 BTST #18,D0 ;TEST B18
002358 67 06 563 BEQ LDIV4 ;SKIP IF BIT ZERO
00235A E288 564 LSR.L #1,D0
00235C E292 565 ROXR.L #1,D2 ;SHIFT RESULT #1 R
00235E 5244 566 ADDQ.W #1,D4 ;ADD 1 TO EXP
567 ;
568 ; ROUND THE RESULT
569 ;
002360 E288 570 LDIV4 LSR.L #1,D0
002362 E292 571 ROXR.L #1,D2 ;SHIFT ONCE
002364 E288 572 LSR.L #1,D0
002366 E292 573 ROXR.L #1,D2 ;B-1 TO CY
002368 64 0C 574 BCC LDIV5 ;SKIP IF NO ROUND
00236A 5282 575 ADDQ.L #1,D2 ;ADD CY TO MANT1
00236C 64 08 576 BCC LDIV5 ;OK IF NO CY
00236E 5240 577 ADDQ.W #1,D0 ;ADD CY TO HI ORD
002370 64 04 578 BCC LDIV5 ;OK IF NO CY
002372 E288 579 LSR.L #1,D0 ;MANT IS $8000...
002374 5344 580 SUBQ.W #1,D4 DECR D4
581 ;
582 ; EXP IN D4; MANT IN D0.W, D2.L
583 ;
002376 3C04 584 LDIV5 MOVE.W D4,D6 ;EXP TO D6 FOR TEST
002378 6B00 FF76 585 BMI RZER1 ;ZERO ON UNDERFLOW
00237C 0246 2000 586 ANDI.W #$2000,D6 ;TEST OVERFLOW
002380 66 14 587 BNE DOVFL ;REPORT OVERFLOW
002382 8978 1902 588 OR D4,S1 ;STORE EXPONENT
002386 31C0 1904 589 MOVE.W D0,M1
00238A 21C2 1906 590 MOVE.L D2,M1+2 ;STORE MANTISSA
00238E 4E75 591 RETN1 RTS
592 ;
002390 7E 02 593 DIV0 MOVEQ #2,D7 ;ERR2 IS DIV BY 0
002392 4EF8 21DA 594 JMP ERROR ;REPORT THE ERROR
595 ;
002396 4EF8 21D8 596 DOVFL JMP ERR1 ;REPORT OVERFLOW
597 ;
598
599 ; START OF 62 BIT FLOATING POINT SUBTRACT
600 ;
00239A 0878 0007 1902 601 LSUB1 BCHG #7,S1 ;TOGGLE D7 OF S1
0023A0 60 0E 602 BRA LADD1 ;FPACC2 IS LOADED
603 ;
0023A2 0878 0007 1902 604 LSUB BCHG #7,S1 ;TOGGLE D7 OF S1
605 ;
606 ; FETCH AN 8 BYTE FP NUMBER TO FPACC#2
607 ;
0023A8 21D8 190A 608 LADD MOVE.L (A0)+,S2 ;A0 IS PTR TO FP#
0023AC 21D8 190E 609 MOVE.L (A0)+,M2+2
610 ;
611 ; PERFORM A 62 BIT FLOATING POINT SIGNED ADD
612 ;
613 ; FIRST TEST WHETHER EITHER # IS ZERO
614 ;
0023B0 3838 190A 615 LADD1 MOVE.W S2,D4 ;X2 TO D4
0023B4 E34C 616 LSL.W #1,D4 ;TEST FOR ZERO
0023B6 67 D6 617 BEQ RETN1 ;DONE IF X2 = 0
618 ;
0023B8 3038 1902 619 MOVE.W S1,D0 ;X1 TO D0
0023BC E348 620 LSL.W #1,D0 ;TEST FOR ZERO
0023BE 66 0E 621 BNE ADDNZ ;SKIP IF NOT ZERO
622 ;
623 ; FPACC1 IS ZERO; MOVE FPACC2 TO FPACC1 AND EXIT
624 ;
0023C0 21F8 190A 1902 625 MOVE.L S2,S1 ;RESULT IS FPACC2
0023C6 21F8 190E 1906 626 MOVE.L M2+2,M1+2
0023CC 4E75 627 RTS ;RETURN
628 ;
629 ; WE MUST PLACE THE NUMBER WHOSE ABSOLUTE VALUE
630 ; IS GREATEST IN FPACC1. FIRST WE TEST THE
631 ; EXPONENTS, THEN THE MOST SIGNIFICANT 32
632 ; BITS OF THE MANTISSAS AND FINALLY THE LEAST
633 ; SIGNIFICANT 16 BITS OF THE MANTISSAS.
634 ;
0023CE B840 635 ADDNZ CMP.W D0,D4 ;COMPARE EXPS
0023D0 65 36 636 BCS ONEGT2 ;OK IF X1 > X2
0023D2 66 16 637 BNE MSWAP ;SWAP IF X1 < X2
638 ;
0023D4 2238 190C 639 MOVE.L M2,D1
0023D8 B2B8 1904 640 CMP.L M1,D1 ;COMP MOST SIG 32
0023DC 65 2A 641 BCS ONEGT2 ;OK IF M1 > M2
0023DE 66 0A 642 BNE MSWAP ;SWAP IF M1 < M2
643 ;
0023E0 3438 1908 644 MOVE.W M1+4,D2
0023E4 B478 1910 645 CMP.W M2+4,D2 ;COMP LAST 16 BITS
0023E8 64 1E 646 BCC ONEGT2 ;OK IF M1>=M2
647 ;
648
649 ; SWAP THE TWO FLOATING POINT ACCUMULATORS
650 ;
0023EA 2638 1902 651 MSWAP MOVE.L S1,D3 ;FPACC1 TO D3, D7
0023EE 2E38 1906 652 MOVE.L M1+2,D7
0023F2 21F8 190A 1902 653 MOVE.L S2,S1 ;FPACC2 TO FPACC1
0023F8 21F8 190E 1906 654 MOVE.L M2+2,M1+2
0023FE 21C3 190A 655 MOVE.L D3,S2 ;D3, D7 TO FPACC2
002402 21C7 190E 656 MOVE.L D7,M2+2
002406 C144 657 EXG D0,D4 ;EXCHANGE EXPONENTS
658 ;
659 ; ABS(FPACC1) IS NOT > OR = ABS(FPACC2)
660 ;
002408 4241 661 ONEGT2 CLR.W D1 ;CLEAR D1
00240A 9044 662 SUB.W D4,D0 ;D0 = X1 - X2
663
00240C 6700 00A0 664 BEQ.W ALIGND ;SKIP IF EXP'S EQ
665
002410 E248 666 LSR.W #1,D0 ;COMP'SAT FOR LSL'S
667 ;
668 ; FIRST TEST FOR 16 OR FEWER SHIFTS
669 ;
002412 0C40 0010 670 CMPI.W #16,D0 ;16 OR LESS SHIFTS?
002416 65 60 671 BCS LT16 ;SKIP IF < 16
002418 67 4E 672 BEQ EQ16 ;SKIP IF 16 SHIFTS
673 ;
674 ; NEXT TEST FOR 32 OR FEWER SHIFTS
675 ;
00241A 0C40 0020 676 CMPI.W #32,D0 ;32 OR MORE SHIFTS?
00241E 65 32 677 BCS LT32 ;LT32 IF < 32
002420 67 24 678 BEQ EQ32 ;EQ32 IF 32 SHIFTS
679 ;
680 ; FINALLY TEST FOR 33 OR MORE SHIFTS
681 ;
002422 0C40 0030 682 CMPI.W #48,D0 ;TOO MANY SHIFTS?
002426 67 16 683 BEQ EQ48 ;EQ48 IF 48 SHIFTS
002428 6400 FF64 684 BCC RETN1 ;DONE IF DIFF >#48
685 ;
686 ; THERE ARE FEWER THAN 48 BIT SHIFTS BUT > 32
687 ;
00242C 3E38 190C 688 MOVE.W M2,D7
002430 4286 689 CLR.L D6
002432 74 20 690 MOVEQ #32,D2
002434 9042 691 SUB.W D2,D0
002436 E06F 692 LSR.W D0,D7
002438 E351 693 ROXL.W #1,D1 ;SH BIT -1 TO D1
00243A D042 694 ADD.W D2,D0
00243C 60 7C 695 BRA ALIGN3
696 ;
697 ; THE NUMBER OF BIT SHIFTS IS EXACTLY #48
698 ;
00243E 4286 699 EQ48 CLR.L D6 ;SET MANT2 = 0
002440 4247 700 CLR.W D7
002442 72 01 701 MOVEQ #1,D1 ;SET BIT -1 = 1
002444 60 74 702 BRA ALIGN3
703 ;
704 ; THE NUMBER OF SHIFTS IS EXACTLY #32
705 ;
002446 4286 706 EQ32 CLR.L D6
002448 3E38 190C 707 MOVE.W M2,D7
00244C E3F8 190E 708 LSL M2+2 ;SH BIT -1 TO CY
002450 60 66 709 BRA ALIGN2
710 ;
711 ; THERE ARE MORE THAN 16 SHIFTS BUT LESS THAN 32
712 ;
002452 2E38 190C 713 LT32 MOVE.L M2,D7
002456 74 10 714 MOVEQ #16,D2
002458 9042 715 SUB.W D2,D0
00245A E0AF 716 LSR.L D0,D7
00245C E351 717 ROXL.W #1,D1 ;SH BIT -1 TO D1
00245E D042 718 ADD.W D2,D0
002460 2C07 719 MOVE.L D7,D6
002462 4246 720 CLR.W D6
002464 4846 721 SWAP D6
002466 60 52 722 BRA ALIGN3
723 ;
724 ; THE NUMBER OF BIT SHIFTS IS EXACTLY 16
725 ;
002468 4286 726 EQ16 CLR.L D6 ;CLEAR B31-B16
00246A 3C38 190C 727 MOVE.W M2,D6
00246E 3E38 190E 728 MOVE.W M2+2,D7
002472 E3F8 1910 729 LSL M2+4 ;SH BIT -1 TO CY
002476 60 40 730 BRA ALIGN2
731 ;
732 ; THERE ARE FEWER THAN 16 SHIFTS; SELECT BEST WAY
733 ;
002478 2C38 190C 734 LT16 MOVE.L M2,D6
00247C 3E38 1910 735 MOVE.W M2+4,D7 ;MANT 1 TO D6,D7
002480 0C40 0003 736 CMPI.W #3,D0
002484 62 16 737 BHI OV3 ;SKIP IF > 3
738 ;
739 ; SHIFT 1, 2 OR 3 BIT POSITIONS: WHICH?
740 ;
002486 67 06 741 BEQ ASH3 ;SKIP IF = 3
002488 5340 742 SUBQ.W #1,D0
00248A 67 0A 743 BEQ ASH1
00248C 60 04 744 BRA ASH2
745 ;
746 ; THIS IS QUICKEST WAY TO SHIFT 1, 2 OR 3 BITS
747 ;
00248E E28E 748 ASH3 LSR.L #1,D6
002490 E257 749 ROXR.W #1,D7
002492 E28E 750 ASH2 LSR.L #1,D6
002494 E257 751 ROXR.W #1,D7
002496 E28E 752 ASH1 LSR.L #1,D6
002498 E257 753 ROXR.W #1,D7
00249A 60 1C 754 BRA ALIGN2
755 ;
756 ; THERE ARE MORE THAN 3 BIT SHIFTS BUT LESS
757 ; THAN 16; THE # OF SHIFTS IS IN D0.
758 ;
00249C 3606 759 OV3 MOVE.W D6,D3
00249E E0AE 760 LSR.L D0,D6
0024A0 78 10 761 MOVEQ #16,D4 ;- D4 IS EQUAL TO
0024A2 9840 762 SUB.W D0,D4 ;16 - # IF SH'S -
0024A4 E96B 763 LSL.W D4,D3
0024A6 E06F 764 LSR.W D0,D7
0024A8 E351 765 ROXL.W #1,D1 ;SH BIT -1 TO D1
0024AA 8E43 766 OR.W D3,D7
0024AC 60 0C 767 BRA ALIGN3
768 ;
769
0024AE 2C38 190C 770 ALIGND MOVE.L M2,D6 ;MANT2 TO D6, D7
0024B2 3E38 1910 771 MOVE.W M2+4,D7
0024B6 60 02 772 BRA ALIGN3 ;DO NOT TEST CY
773 ;
774 ; MANT2 IS NOW ALIGNED TO CORRESPOND TO EQUAL
775 ; EXPONENTS FOR FPACC1 AND FPACC2.
776 ;
0024B8 E351 777 ALIGN2 ROXL.W #1,D1 ;SH BIT -1 TO D1
0024BA 2838 1904 778 ALIGN3 MOVE.L M1,D4 ;MANT1 TO D4, D5
0024BE 3A38 1908 779 MOVE.W M1+4,D5
780 ;
781 ; TEST THE SIGNS; SUBTRACT IF DIFFERENT
782 ;
0024C2 3038 1902 783 MOVE.W S1,D0
0024C6 D078 190A 784 ADD.W S2,D0
0024CA 6B 3E 785 BMI FSUB2 ;DIFF SIGNS; SUB
786 ;
787 ; THE SIGNS ARE THE SAME; PERFORM ADDITION
788 ;
0024CC DA47 789 ADD.W D7,D5 ;ADD M2 TO M1
0024CE D986 790 ADDX.L D6,D4
0024D0 64 1E 791 BCC ARND ;ARND IF NO OVFL
792 ;
0024D2 E294 793 ROXR.L #1,D4 ;SHIFT MANT1 R TO
0024D4 E255 794 ROXR.W #1,D5 ;COMPENSATE OVFL
0024D6 64 06 795 BCC COVF1 ;NO ROUND IF CY=0
796 ;
0024D8 5245 797 ADDQ.W #1,D5 ;ADD #1 TO 1ST 16;
0024DA 64 02 798 BCC COVF1 ;COVF1 IF CY = 0 --
0024DC 5284 799 ADDQ.L #1,D4 ;NO OVFL POSS HERE
800 ;
801 ; ADJUST EXPONENT TO COMPENSATE FOR OVERFLOW
802 ;
0024DE 5278 1902 803 COVF1 ADDQ.W #1,S1 ;ADD 1 TO EXP
0024E2 0838 0005 1902 804 BTST #5,S1 ;TEST FOR OVERFLOW
0024E8 67 16 805 BEQ ADDX ;OK IF NO OVFL
806 ;
0024EA 7E 01 807 MOVEQ #1,D7 ;ERR1 = OVERFLOW
0024EC 4EF8 21DA 808 JMP ERROR
809 ;
0024F0 E249 810 ARND LSR.W #1,D1 ;BIT -1 TO CY
0024F2 64 0C 811 BCC ADDX
0024F4 5245 812 ADDQ.W #1,D5
0024F6 64 08 813 BCC ADDX
0024F8 5284 814 ADDQ.L #1,D4
0024FA 64 04 815 BCC ADDX
816 ;
817 ; SET MANT1 = $8000 0000 0000
818 ;
0024FC E294 819 ROXR.L #1,D4 ;CY TO MSB
0024FE 60 DE 820 BRA COVF1 ;ADJ EXP
821 ;
002500 21C4 1904 822 ADDX MOVE.L D4,M1 ;STORE MAN1
002504 31C5 1908 823 MOVE.W D5,M1+4
002508 4E75 824 RTS ;ADDITION DONE
825 ;
826
827 ; THE SIGNS ARE DIFFERENT; SUBTRACT
828 ;
00250A 3001 829 FSUB2 MOVE.W D1,D0 ;BIT -1 TO D0
00250C 4E71 830 NOP ;POSS ADDQ.W #1,D0
00250E E248 831 LSR.W #1,D0 ;SH BIT-1 INTO CY
002510 9B47 832 SUBX.W D7,D5 ;D4,5 - M1 - M2
002512 9986 833 SUBX.L D6,D4 ;NO UNDFL POSS
834 ;
835 ; NORMALIZE; MANT1 IS IN D4.L & D5.W; S1,X1 IN MEM
836 ; BIT -1 IS IN DATA REG 1, BIT 1
837 ;
002514 2604 838 NORM MOVE.L D4,D3 ;TEST B31-B16
002516 6B E8 839 BMI ADDX ;OK OF B31 - 1
002518 5378 1902 840 SUBQ.W #1,S1 ;DECR EXP
00251C E249 841 LSR.W #1,D1 ;SH BIT -1 INTO M1
00251E E355 842 ROXL.W #1,D5
002520 E394 843 ROXL.L #1,D4
002522 6B 4C 844 BMI SUBX ;SKIP IF NORM'D
845 ;
002524 66 1A 846 BNE NORM1 ;NORM1 IF B47-16>0
847 ;
848 ; THE MOST SIG 32 BITS OF THE MANT ARE ZERO
849 ;
002526 72 20 850 MOVEQ #32,D1 ;SHIFT CTR = #32
002528 3805 851 MOVE.W D5,D4 ;TEST LAST 16 BITS
00252A 6700 FDC4 852 BEQ RZER1 ;RESULT IS ZERO
00252E 6B 06 853 BMI SHW1 ;SHW1 IF NORML'ZD
854 ;
855 ; SHIFT MANT1 (16 BITS) LEFT UNTIL NORMALIZED)
856 ;
002530 5241 857 SHW ADDQ #1,D1 ;INCR SHIFT CTR
002532 E34C 858 LSL.W #1,D4 ;SHIFT MANT 1 LEFT
002534 6A FA 859 BPL SHW ;DO UNTIL NORM'D
860 ;
861 ; MANT1 (16 BITS) IS NOT NORMALIZED; STORE IT
862 ;
002536 31C4 1904 863 SHW1 MOVE.W D4,M1 ;STORE B47-B32
00253A 42B8 1906 864 CLR.L M1+2 ;CLR B31-B0
00253E 60 2C 865 BRA SLT16X ;DECR X1 & EXIT
866 ;
002540 0C84 00010000 867 NORM1 CMPI.L #$10000,D4
002546 64 1A 868 BCC SLT16 ;SHIFT LESS THAN 16
869 ;
870 ; D4 IS < $10000; SWAP HALVES AND
871 ; GATHER 32 BIT MANT1 IN D4.
872 ;
002548 72 10 873 MOVEQ #16,D1 ;SHIFT COUNT = 16
00254A 4844 874 SWAP D4
00254C 3805 875 MOVE.W D5,D4 ;32 BIT M1 IN D4
876 ;
877
878 ; TEST WHETHER 32 BIT MANT1 IS NORMALIZED
879 ;
00254E 2A04 880 MOVE.L D4,D5 ;TEST BIT #31
002550 6B 06 881 BMI SHL1 ;SHL1 IF B31 = 1
882 ;
883 ; SHIFT MANT1 (32 BITS) LEFT UNTIL NORMALIZED
884 ;
002552 5241 885 SHL ADDQ.W #1,D1 ;INCR SHIFT CTR
002554 E38C 886 LSL.L #1,D4 ;SHIFT MANT LEFT
002556 6A FA 887 BPL SHL ;LOOP UNTIL B31 = 0
888 ;
889 ; MANT1 (32 BITS) IS NOT NORMALIZED; STORE IT
890 ;
002558 21C4 1904 891 SHL1 MOVE.L D4,M1 ;STORE MANT1
00255C 4278 1908 892 CLR.W M1+4 ;CLR B15-0
002560 60 0A 893 BRA SLT16X ;DECR EXP & EXIT
894 ;
895 ; THERE ARE FEWER THAN 16 BIT SHIFTS
896 ; SHIFT MANT1 (48 BITS) LEFT UNTIL NORMALIZED
897 ;
002562 4241 898 SLT16 CLR.W D1 ;SHIFT COUNT = 0
002564 5241 899 SLT16A ADDQ.W #1,D1 ;INCR SHIFT CTR
002566 E34D 900 LSL.W #1,D5 ;SHIFT MANT1 LEFT
002568 E394 901 ROXL.L #1,D4
00256A 6A F8 902 BPL SLT16A ;LOOP UNTIL B31 =1
903 ;
904 ; MANT1 (48 BITS) IS NOW NORMALIZED
905 ;
906 ; SUBTRACT THE SHIFT COUNT FROM THE EXPONENT
907 ; AND THEN TEST FOR UNDERFLOW.
908 ;
00256C 9378 1902 909 SLT16X SUB.W D1,S1 ;DECR EXP
002570 0838 0006 1902 910 SUBX BTST #6,S1 ;TEST FOR UNDFL
002576 6600 FD78 911 BNE RZER1 ;ZERO ON UNDFL
00257A 21C4 1904 912 MOVE.L D4,M1 ;STORE MANT1
00257E 31C5 1908 913 MOVE.W D5,M1+4
914 ;
002582 4E75 915 RTS ;NORM OR SUB DONE
916 ;
002584 <140> 917 DS.L 80
918 ;
0026C4 00000000 919 N DC.L $00000000 ;LONG WORD
@ 000026C8 920 NSQD EQU N+4 ;N SQUARED
@ 000026CC 921 ARYST EQU NSQD+4 ;WORD
@ 000026CE 922 CPTR EQU ARYST+2 ;WORD
@ 000026D0 923 RPTR EQU CPTR+2 ;START OF ROW VECT
# 00001926 924 FCTR EQU EXPADD