TweetFollow Us on Twitter

68881 Access
Volume Number:4
Issue Number:4
Column Tag:Forth Forum

Direct 68881 Floating Point Access

By Jörg Langowski, MacTutor Editorial Board, Grenoble, France

Being the proud owner of a MacII since the beginning of this year, I was - like so many others - disappointed at the relative slowness of the SANE package. Even with the floating point coprocessor, the speedup is only a factor of 5-10 compared to the Mac SE. The coprocessor itself allows you to go much faster than that, and it is Apple’s SANE implementation that slows down the operations.

The reason for this is, of course, that Apple is trying to guarantee the ‘compatibility’ of the SANE on the MacII with the old SANE implementation. That means that the results are supposed to be the same, down to the least significant bit (or even to the last guard bit?). The 68881 uses different algorithms for calculating transcendental functions than SANE does, therefore some of its built-in operations could not be used and had to be replaced by software. Of course, that slows down things a lot.

As a side note, I’m not at all in favor of such a strategy. Artificially restraining a high performance chip just because its results, although accurate enough, don’t match the old - also accurate - results to the last bit seems a little exaggerated. Stable numerical algorithms should take into account the possibility that the hardware changes slightly and the machine errors are different, and they should be immune against such changes; or at least the new SANE should have had an option built in that uses the 68881 directly! [Amen to that statement! -Ed]

Many of the development systems for the Macintosh now come with the possibility to generate code that supports the floating point coprocessor directly, many others don’t; working with Forth, we don’t have a real problem since we can easily redefine our floating point operators. This month I’ll show you how to do that.

The 68881

Let’s first have a look at the floating point coprocessor itself.

The 68881 is accessed from the 68020 in a special address area. When the 68020 encounters an instruction of the form $Fxxx (previously the F line trap), it will set its function code lines (pins FC0-FC2) all to high, indicating ‘CPU space’. It will then exchange information with the coprocessor’s internal registers to perform the floating point operation requested.

This information exchange occurs automatically, it is part of the 68020’s design; when using the floating point instructions, you don’t notice the communication between the two processors at all. The 68881 appears as an extension to the 68020, just as if we had a new set of registers available, with special instructions operating on them.

The registers FP0-FP7 can each hold one extended precision (80-bit) floating point number, in the format given by the IEEE standard: bits 0-63 contain the mantissa, 64-78 the 15-bit exponent offset by 16383, and bit 79 the sign. The instruction set of the 68881 allows you to do floating point operations on any or between any two of these registers, and transfer data between them, the 68020’s registers and memory.

Mach2’s assembler fully supports all 68881 instructions. The redefinition of the words in the SANE vocabulary is therefore quite straightforward. Register D7 is used by Mach2 as the floating point stack pointer, all we have to do is to transfer floating point numbers from the FP stack to the 68881’s registers, do the FP operation and transfer back the result.

The 68881 expects floating point numbers in a different format than SANE does. In order to keep FP numbers aligned to the boundaries of a 32-bit long word, which speeds up operations, an extended precision number in memory will be 96 bits long instead of 80; there is a 16 bit gap between the 64-bit mantissa and the 16-bit sign and exponent field. Since SANE and the floating point stack in Mach2 use 80 bit numbers, we have to convert their format when we use the coprocessor.

Listing 1 provides the macros f>2, f>1 and 1>f for this purpose. The general format for a binary floating point operation is then

 f>2  
 fop.x  FPn, FPm 
 1>f

where fop.x is an extended format floating point instruction that operates on floating point registers FPn and FPm. The example always uses registers FP0 and FP1. Unary operations are encoded the same way, using only FP0.

In the example, I provided a new vocabulary f68881 that contains redefinitions of the most important SANE operations for the 68881. Of course, the concept can be far extended. We have eight registers at our disposition and can use them to optimize more complicated numerical algorithms, using only assembly language. I might give some examples how to do this in a later column.

For the moment, let’s content ourselves with the speed improvement that we have achieved so far, which is already remarkable. Some simple benchmarks are listed at the end of listing 1, and the results are given here:

( MacII, direct 68881 access, 100000 loops each )

bmark1 2 Secs 18 Ticks ok <0> [0]

bmark2 4 Secs 48 Ticks ok <0> [0]

bmark3 4 Secs 14 Ticks ok <0> [0]

bmark4 4 Secs 17 Ticks ok <0> [0]

bmark5 4 Secs 14 Ticks ok <0> [0]

( MacII, SANE w/68881, 10000 loops each )

smark1 15 Ticks ok <0> [0]

smark2 37 Secs 12 Ticks ok <0> [0]

smark3 24 Ticks ok <0> [0]

smark4 1 Secs 33 Ticks ok <0> [0]

smark5 1 Secs 33 Ticks ok <0> [0]

( Mac +, SANE, 10000 loops each )

ok <0> [0]

smark1 24 Ticks ok <0> [0]

smark2 181 Secs 54 Ticks ok <0> [0]

smark3 49 Ticks ok <0> [0]

smark4 4 Secs 47 Ticks ok <0> [0]

smark5 5 Secs 14 Ticks ok <0> [0]

For the Mac+, the fnull1 and fnull2 operations had been replaced by simple fdrops. As you see, the speedup going from Mac+ to MacII’s SANE is not so breathtaking: a factor of 6 for the exponential, 4 for addition and subtraction; but when we access the 68881 directly, we gain another factor of 3 for simple addition and multiplication and 78 for the exponential. It is in the calculation of the transcendentals where the 68881 really shines.

Pop up menus

Someone approached me lately on the question of how to do pop up menu selection. Since the technical notes contain only sketchy references to popup menus at the time I write this (e.g. TN156, TN172), I’d like to give you a practical example how to use pop up menus from Mach2 in a simple way.

Listing 2 explains the process. The PopUpMenuSelect trap takes four parameters:

- a handle to the menu to be displayed (32 bits),

- the top and left global coordinate of the point at which to display the menu (2*16 bits),

- the menu item which should be positioned at that point for the default selection.

Although Mach2 knows the trap name, the interface to this routine is not (yet) correct, so we have to redefine it in assembler. Note that the point returned by the @mouse function is in local coordinates, while PopUpMenuSelect expects it in global coordinates.

The example defines a menu using the Mach2 interface; the menu is created with -1 as the insertion parameter (-1 150 mymenu BOUNDS) so that after insertion into the tasks’s menu bar the menu will stay invisible (just as we did for the hierarchical menus). Note that a pop up menu has to be inserted into the menu bar before using it.

The content handler for the default Mach2 window is then rewritten so that on a mouse down event it will select the example pop up menu. The menu handler will just beep a number of times depending on the item selected. dopop activates the new content handler while nopop deactivates it.

Feedback dept.

This letter comes from Vassili Dzuba, Paris:

“In January’s issue ‘Mousehole Report’, Alan Dall put in his wish list the ability to define ‘ghost copies’ of applications. Even without Unix’ capability of defining links, this can be done with a small program using the _Launch trap. This program takes only 1K on the disk. The path name of the application to launch is stored in ‘STR ‘ resource 1000. It’s possible to set the creator and the bundle bit of the ghost to have it share the same icon as the real thing. Of course, double-clicking on a document can then launch the ghost instead of the application, but the slowing down is only marginal.

The program is the following

(using MPW’s assembler):

 INCLUDE‘traps.a’
ghost MAIN
 MOVE.W #0,-(SP) 
 ; the context data (_launch parameter)
 MOVE.L #’STR ‘,-(SP)
 ; 1st parameter of GetResource
 MOVE.W #1000,-(SP)
 ; 2nd parameter of GetResource
 _GetResource
 ; handle to string in (SP)
 TST.L  (SP)
 ; test if null handle (no resource available)
 BEQ.B  exit
 ; if null, go to exit
 MOVE.L (SP),A0
 MOVE.L (A0),(SP)
 ; handle dereferenced
 MOVE.L SP,A0
 ; stack pointer in A0
 _Launch
exit  _ExitToShell
 END

The resource file is something like this (using Rez format):

#include “types.r”
resource ‘STR ‘ (1000) {
 “Sys:myDirectory:MyApp”
};

A ghost can be easily created using a small shell script (assuming the original ghost’s directory being {MPW}dev) which sets up the string resource:

duplicate {MPW}’dev:ghost’ {2}
echo ‘#include “types.r”’n
‘resource ‘’’STR ‘’’ (1000) { “‘{1}’” };’
| rez -a -o {2}

Assuming this script is named ‘summon’, the creation in the current directory of a ghost of MacPaint would be something like:

summon ‘sys:appli ƒ:mac paint’ ‘macpaint.Ghost’

Sincerely yours”

Thank you, Vassili, for this helpful little utility.


Listing 1: direct access 68881 floating point words for Mach2
\ 68881 access, © J. Langowski/MacTutor Jan 1988

only forth also assembler also sane
vocabulary f68881
also f68881 definitions

code f>2
 add.l  #20,d7
 move.l d7,a0
 move.l -(a0),-(a7); move mantissa
 move.l -(a0),-(a7); in two 32-bit chunks
 subq.l #2,a7    ; 16-bit gap
 move.w -(a0),-(a7); move exponent + sign
 fmove.x(a7)+,fp0; transfer from stack to fp0
 move.l -(a0),-(a7); same for fp1...
 move.l -(a0),-(a7)
 subq.l #2,a7
 move.w -(a0),-(a7)
 fmove.x(a7)+,fp1
 add.l  #10,a0 ; a0 points to 2nd fp stack item
 rts
end-code mach

code f>1
 add.l  #10,d7
 move.l d7,a0
 move.l -(a0),-(a7)
 move.l -(a0),-(a7)
 subq.l #2,a7
 move.w -(a0),-(a7)
 fmove.x(a7)+,fp0
 rts
end-code mach

code 1>f
 fmove.xfp0,-(a7)
 move.w (a7)+,(a0)+; transfer exponent + sign
 addq.l #2,a7    ; skip16 bit gap
 move.l (a7)+,(a0)+; transfer mantissa 
 move.l (a7)+,(a0)+; in 2 steps
 sub.l  #10,d7   ; adjust FP stack pointer
 rts
end-code mach

( note: f>1 or f>2 and 1>f should always occur in pairs since 1>f expects 
A0 to point to second floating point stack position; this is assured 
by f>1 and f>2 )

code f+
 f>2
 fadd.x fp1,fp0
 1>f
 rts
end-code

code f-
 f>2
 fsub.x fp1,fp0
 1>f
 rts
end-code

code f/
 f>2
 fdiv.x fp1,fp0
 1>f
 rts
end-code

code f*
 f>2
 fmul.x fp1,fp0
 1>f
 rts
end-code

code fmod
 f>2
 fmod.x fp1,fp0
 1>f
 rts
end-code

code frem
 f>2
 frem.x fp1,fp0
 1>f
 rts
end-code

code fabs
 f>1
 fabs.x fp0
 1>f
 rts
end-code

code facos
 f>1
 facos.xfp0
 1>f
 rts
end-code

code fasin
 f>1
 fasin.xfp0
 1>f
 rts
end-code

code fatan
 f>1
 fatan.xfp0
 1>f
 rts
end-code

code fatanh
 f>1
 fatanh.x fp0
 1>f
 rts
end-code

code fcos
 f>1
 fcos.x fp0
 1>f
 rts
end-code

code fcosh
 f>1
 fcosh.xfp0
 1>f
 rts
end-code

code fe^x
 f>1
 fetox.xfp0
 1>f
 rts
end-code
 
code fe^x-1
 f>1
 fetoxm1.x fp0
 1>f
 rts
end-code

code fgetexp
 f>1
 fgetexp.x fp0
 1>f
 rts
end-code

code fgetman
 f>1
 fgetexp.x fp0
 1>f
 rts
end-code

code fint
 f>1
 fint.x fp0
 1>f
 rts
end-code

code fintrz
 f>1
 fintrz.x fp0
 1>f
 rts
end-code

code fln
 f>1
 flogn.x  fp0
 1>f
 rts
end-code

code fln+1
 f>1
 flognp1.x fp0
 1>f
 rts
end-code

code flog10
 f>1
 flog10.x fp0
 1>f
 rts
end-code

code flog2
 f>1
 flog2.x  fp0
 1>f
 rts
end-code

code fneg
 f>1
 fneg.x fp0
 1>f
 rts
end-code

code fsin
 f>1
 fsin.x fp0
 1>f
 rts
end-code

code fsinh
 f>1
 fsinh.x  fp0
 1>f
 rts
end-code

code fsqrt
 f>1
 fsqrt.x  fp0
 1>f
 rts
end-code

code ftan
 f>1
 ftan.x fp0
 1>f
 rts
end-code

code ftanh
 f>1
 ftanh.x  fp0
 1>f
 rts
end-code

code f10^x
 f>1
 ftentox.x fp0
 1>f
 rts
end-code

code f2^x
 f>1
 ftwotox.x fp0
 1>f
 rts
end-code

fp

also forth definitions
code fnull1
 f>1
 1>f
 rts
end-code

code fnull2
 f>2
 1>f
 rts
end-code

: bmark1 counter 1.0 
 100000 0 do fdup fnull1 fdrop loop 
timer fdrop ;

: bmark2 counter 4.3352 
 100000 0 do fdup fe^x fdrop loop 
timer fdrop ;

: bmark3 counter 
 3.5 4.5 100000 0 do fover fover fnull2 fdrop loop 
timer fdrop fdrop ;

: bmark4 counter 
 3.5 4.5 100000 0 do fover fover f+ fdrop loop 
timer fdrop fdrop ;

: bmark5 counter 
 3.5 4.5 100000 0 do fover fover f* fdrop loop 
timer fdrop fdrop ;

also sane

: smark1 counter 
 1.0 10000 0 do fdup fnull1 fdrop loop 
timer fdrop ;

: smark2 counter 
 4.3352 10000 0 do fdup fe^x fdrop loop 
timer fdrop ;

: smark3 counter 
 3.5 4.5 10000 0 do fover fover fnull2 fdrop loop 
timer fdrop fdrop ;

: smark4 counter 
 3.5 4.5 10000 0 do fover fover f+ fdrop loop 
timer fdrop fdrop ;

: smark5 counter 
 3.5 4.5 10000 0 do fover fover f* fdrop loop 
timer fdrop fdrop ;
Listing 2: Pop up menus
\ popup menu interface from Forth
\ © J. Langowski/MacTutor Jan 1988

\ FUNCTION PopUpMenuSelect 
\ (menu: MenuHandle; top, left, popUpItem: INTEGER):
\LONGINT;
\  INLINE $A80B;

code popup ( hMenu top left item# | menuID item  -- )
 exg  d4,a7
 clr.l  -(a7)
 move.l 12(a6),-(a7) \ handle
 move.w 10(a6),-(a7) \ top
 move.w 6(a6),-(a7)\ left
 move.w 2(a6),-(a7)\ item
 adda.l #16,A6
 _popupmenuselect
 clr.l  d0
 clr.l  d1
 move.w (a7)+,d0
 move.w (a7)+,d1
 exg  d4,a7
 move.l d0,-(a6)
 move.l d1,-(a6)
 rts
end-code

CODE  @MOUSE
    SUBQ.L    #4,A6
    MOVE.L    A6,-(A7)
    _GETMOUSE
    RTS
END-CODE

CODE unpack
 MOVE.L (A6),D0
 CLR.L  D1
 MOVE.W D0,D1
 CLR.W  D0
 SWAP.W D0
 MOVE.L D0,(A6)
 MOVE.L D1,-(A6)
 RTS
END-CODE MACH

108 user taskmenubar
152 user content-hook

NEW.MENU myMenu
“ TestMenu” myMenu TITLE
-1 150 myMenu BOUNDS \ invisible menu
“ Item 1;Item 2;Item 3” myMenu ITEMS

taskmenubar @ mymenu add
call drawmenubar

: beep 
 ?dup if 
 0 do 5 call sysbeep loop 
 then
;

: content-handler { | pt -- }
 @mouse -> pt
 ^ pt call localtoglobal
 mymenu @
 pt unpack
 1
 popup
 beep drop
 run-content
;

: dopop [‘] content-handler content-hook ! ;
: nopop [‘] run-content content-hook ! ;
 

Community Search:
MacTech Search:

Software Updates via MacUpdate

BlueStacks 4.140.13 - Run Android applic...
BlueStacks App Player lets you run your Android apps fast and fullscreen on your Mac. Feature comparison chart Version 4.140.13: Highlights/Bug Fixes: Feel free to use BlueStacks as your go to... Read more
Adobe Premiere Pro CC 2020 14.0.1 - Digi...
Premiere Pro CC 2020 is available as part of Adobe Creative Cloud for as little as $52.99/month. The price on display is a price for annual by-monthly plan for Adobe Premiere Pro only Adobe Premiere... Read more
VirtualBox 6.1.2 - x86 virtualization so...
VirtualBox is a family of powerful x86 virtualization products for enterprise as well as home use. Not only is VirtualBox an extremely feature rich, high performance product for enterprise customers... Read more
RoboForm 8.6.8 - Password manager; syncs...
RoboForm is a password manager that offers one-click login, mobile syncing, easy form filling, and reliable security. Password Manager. RoboForm remembers your passwords so you don't have to! Just... Read more
Postbox 7.0.11 - Powerful and flexible e...
Postbox is a new email application that helps you organize your work life and get stuff done. It has all the elegance and simplicity of Apple Mail, but with more power and flexibility to manage even... Read more
calibre 4.9.0 - Complete e-book library...
Calibre is a complete e-book library manager. Organize your collection, convert your books to multiple formats, and sync with all of your devices. Let Calibre be your multi-tasking digital librarian... Read more
Notability 4.2 - Note-taking and annotat...
Notability is a powerful note-taker to annotate documents, sketch ideas, record lectures, take notes and more. It combines, typing, handwriting, audio recording, and photos so you can create notes... Read more
FoldersSynchronizer 5.0.1 - Synchronize...
FoldersSynchronizer is a popular and useful utility that synchronizes and backs-up files, folders, disks and boot disks. On each session you can apply special options like Timers, Multiple Folders,... Read more
Sketch 62 - Design app for UX/UI for iOS...
Sketch is an innovative and fresh look at vector drawing. Its intentionally minimalist design is based upon a drawing space of unlimited size and layers, free of palettes, panels, menus, windows, and... Read more
ScreenFlow 9.0.2 - Create screen recordi...
ScreenFlow is powerful, easy-to-use screencasting software for the Mac. With ScreenFlow you can record the contents of your entire monitor while also capturing your video camera, microphone and your... Read more

Latest Forum Discussions

See All

Slingsters is a physics-based puzzler fo...
Slingsters is a physics-based puzzle game where the aim is to collect various different monsters by flinging them from one side of a level to the other and into a box. It's also the first game from Nappy Cat and is available now for iOS and... | Read more »
Spiritwish's latest update sees the...
A sizeable update has hit Nexon's MMORPG Spiritwish today. It brings a new game mode, characters and there will also be a special event to celebrate the update with a firework display. [Read more] | Read more »
Maze Machina, a turn-based puzzler from...
The latest game from Arnold Rauers also known as Tiny Touch Tales is now available. You may be familiar with one of his many excellent titles such as Card Crawl, Enyo and Card Thief. His latest endeavour is called Maze Machina and you can grab it... | Read more »
Mario Kart Tour's Ice Tour races to...
Can you believe Mario Kart Tour is already on its 9th tour? The game only launched back in September, and since then it's become increasingly tricky to keep on top of the amount of new content Nintendo is pumping out. [Read more] | Read more »
Apple Arcade: Ranked - Top 50 [Updated 1...
In case you missed it, I am on a quest to rank every Apple Arcade game there is. [Read more] | Read more »
Marvel Future Fight's latest update...
Marvel Future Fight's latest update has added an all-new team of heroes to recruit and do battle with. The 'Warriors of the Sky' include Blue Dragon, War Tiger, Sun Bird, and Shadow Shell. As is the norm, each character comes with their own unique... | Read more »
Klee: Spacetime Cleaners is a fast-paced...
Klee: Spacetime Cleaners is a fast-paced auto-shooter that sports a cute retro aesthetic thathad racked up an impressive 100,000 pre-registers prior to its release. It's available now for both iOS and Android. [Read more] | Read more »
Hearthstone's latest solo adventure...
Blizzard has unveiled a plethora of details about its upcoming expansion for its popular card game Hearthstone. It's called Galakrond's Awakening and will bring the Year of the Dragon storyline to a close. It's available now for pre-purchase ahead... | Read more »
Cultist Simulator's Dancer DLC laun...
Cultist Simulator's Dancer DLC is set to launch for iOS and Android on January 22nd. It revolves around the occult cabaret known as the 'Ecdysis Club', where "the distinction between pleasure and pain is as delicate and essential as the human skin... | Read more »
Death Comes True releases a new characte...
Death Comes True is an FMV murder mystery from Kazutaka Kodaka, the creator of Danganronpa. It sees you playing as an amnesiac young man, called Makoto Karaki, who wakes up in a mysterious hotel to find that he's being hunted for a series of... | Read more »

Price Scanner via MacPrices.net

New Verizon deal: Apple iPhone XR for $300 of...
Switch to Verizon and sign up with one of their Unlimited plans, and Verizon will take $300 off the price of an Apple iPhone XR (regularly $749), plus get a free $200 prepaid Mastercard. This is an... Read more
Amazon’s popular AirPods sale is back with mo...
Amazon has new 2019 Apple AirPods on sale today ranging up to $40 off MSRP, starting at $129, as part of their popular Apple AirPods sale. Shipping is free: – AirPods Pro: $234.98 $15 off MSRP –... Read more
Apple’s top of the line 10.5″ 256GB WiFi + Ce...
B&H Photo has the top of the line 10.5″ 256GB WiFi + Cellular iPad Air on sale for $599 shipped. That’s $180 off Apple’s MSRP for this model and the cheapest price available. Overnight shipping... Read more
Apple’s refurbished iPad Pros are the cheapes...
Apple has Certified Refurbished 11″ iPad Pros available on their online store for up to $220 off the cost of new models. Prices start at $679. Each iPad comes with a standard Apple one-year warranty... Read more
Just in: Take $100 off the price of the 3.0GH...
Apple resellers are offering new 2018 6-Core Mac minis for $100 off Apple’s MSRP today, only $999. B&H Photo has 6-Core Mac minis on sale for $100 off Apple’s standard MSRP. Overnight shipping is... Read more
Apple has 4-core and 6-core 2018 Mac minis av...
Apple has Certified Refurbished 2018 Mac minis available on their online store for $120-$170 off the cost of new models. Each mini comes with a new outer case plus a standard Apple one-year warranty... Read more
Amazon offers $200 discount on 13″ MacBook Ai...
Amazon has new 2019 13″ MacBook Airs with 256GB SSDs on sale for $200 off Apple’s MSRP, now only $1099, each including free shipping. Be sure to select Amazon as the seller during checkout, rather... Read more
Apple’s AirPods drop to $129 again at these r...
Apple resellers are offering $30 discounts on Apple AirPods with Charging Case, with prices at $129. These prices are the cheapest new AirPods prices currently available from any Apple reseller: (1)... Read more
Save up to $250 on an iPhone XS with these Ce...
Apple is now offering Certified Refurbished iPhone XS models for up to $350 off MSRP with prices starting at $699. Each iPhone is unlocked and comes with Apple’s standard one-year warranty and a new... Read more
B&H offers 13″ MacBook Airs for $150 off...
B&H Photo has 13″ 128GB MacBook Airs on sale for $150 off Apple’s MSRP, only $949. Overnight shipping is free to many locations in the US: – 13″ 1.6GHz/128GB MacBook Air Space Gray: $949.99 $150... Read more

Jobs Board

Best Buy *Apple* Computing Master - Best Bu...
**745058BR** **Job Title:** Best Buy Apple Computing Master **Job Category:** Store Associates **Store NUmber or Department:** 001080-Lake Charles-Store **Job Read more
Geek Squad *Apple* Consultation Professiona...
**756640BR** **Job Title:** Geek Squad Apple Consultation Professional **Job Category:** Store Associates **Store NUmber or Department:** 000484-Manchester-Store Read more
*Apple* Phenology Coordinator - Montana Stat...
…Rachel Leisso at ### or ###@montana.edu Classification Title Working Title Apple Phenology Coordinator Brief Position Overview This position provides support for Read more
Business Development Specialist - *Apple* -...
Responsible for driving sales growth specifically for the Apple product line within CDW's account base. Primarily working with CDW and Apple sales teams and Read more
Geek Squad *Apple* Consultation Professiona...
**757640BR** **Job Title:** Geek Squad Apple Consultation Professional **Job Category:** Store Associates **Store NUmber or Department:** 000802-Las Cruces-Store Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.