TweetFollow Us on Twitter

Forth SANE
Volume Number:1
Issue Number:1
Column Tag:FORTH FORUM

“Forth Goes SANE”

By Joerg Langowski

“Forth Goes SANE”

One of the little unexpected features of the Macintosh that was very important to me for doing some actual calculations is the built-in floating point package. There is a full set of floating point routines, ranging from the four basic operations up to trigonometric and other functions, built right into the Mac, and they can be called up through a standard toolbox calling procedure and turn out to be reasonably (if not really breathtakingly) fast. If you want to try out the floating point routines and have access to MacForth 1.1, the following should give you some useful information. MacForth level 2 supposedly makes use of the same routines, but it was not available at the time that this was written.

Let’s first look at some general features. The floating point package, called FP68K by Apple, is based on a proposed IEEE floating point standard P754. It can work on 32, 64 and 80-bit floating point numbers and 16, 32, and 64-bit integers. Some of the operations that it supports are summarized in Table 1. (Because of space limitations, this table is by no means complete, but I tried to list the most important operations.) All calculations are internally done with 80-bit accuracy; this seems spectacular, but a little overdone. Speed could probably be improved a lot, had Apple allowed for working with lower precision.

Floating point operations are always called in the same manner: the addresses of the two arguments, source and destination, are pushed on the stack, followed by the opcode; then the toolbox trap _FP68K (for the basic operations) or _ELEMS68K (for the more complicated functions) is called. The result will be deposited in the destination address, which is overwritten. To understand the calling procedure better, let us see how toolbox traps are called from MacForth.

There are three types of toolbox traps in the Macintosh. Operating system traps expect a buffer pointer in register A0 and return an I/O result in D0; Pascal procedures expect their parameters on the stack, and Pascal functions expect a space for their result on the bottom of the stack, followed by all the parameters. MacForth 1.1 provides predefined words for all three trap types; they will be described in detail in the next issue of MacTech. The floating point package is called as a Pascal procedure, with its parameters on the stack. Since stack items in MacForth are 32 bits in length, while some of the toolbox procedures expect 16 bit parameters, there exist three different Forth words for Pascal-type calls, depending whether there are none, one or two 16-bit items on top of the stack: MT, W>MT and 2W>MT.

The floating point routines always expect one 16 bit parameter on top, all other parameters (up to three) are 32 bits long. The MacForth word to call these routines therefore would be W>MT. The trap addresses are $A9EB for FP68K and $A9EC for ELEMS68K. (These are, actually, the addresses of Package 4 and Package 5 of the Operating System Packages). We can now define our trap calls:

HEX
:  A9EB  W>MT FP68K ;
:  A9EC  W>MT ELEMS68K ;

Then we can call a floating point operation by pushing the parameters on the stack, followed by the opcode, and executing FP68K or ELEMS68K. As an example, if we had defined the 10-byte variables SOURCE and DESTINATION:

SOURCE  CREATE  10  ALLOT 
DESTINATION  CREATE  10  ALLOT

and had put real numbers into both of them, we would add SOURCE into DESTINATION by executing:

SOURCE  DESTINATION  0  FP68K 

after which operation DESTINATION would contain the 80-bit result of the addition, while the contents of SOURCE would be unchanged. A function from the ELEMS68K package would be called in an equally simple way, e.g. the natural logarithm of DESTINATION is obtained by saying DESTINATION 0 FP68K .

The 16-bit opcode consists of two parts. The high order byte gives the format of the SOURCE operand (except for opcodes $9 and $10, see table 1), the low order byte specifies the operation. Listing 1 defines some Forth words that call the most important floating point operations through toolbox calls with the appropriate opcode on the stack.

There is one operation that deserves special attention, and that is the floating point - decimal conversion routine. This routine expects three parameters underneath the opcode: deepest in the stack is a pointer to a ‘format record’, followed by the source variable pointer, and then the destination pointer. For a conversion from a real number to a decimal number, the source variable is 10-byte floating point and the destination variable consists of a 2 byte integer which is 0 for positive and >256 for negative numbers, a 2 byte signed integer which contains the exponent, a 1 byte field which contains the length and a 20 byte field which contains the significant digits of the mantissa. The format record is, for our purposes, a 4 byte integer which gives the number of significant digits to be used in the conversion. Example, assume that Y points to the real number 2.345, DECSTRING to a 25-byte array and FORMAT to a 4-byte integer containing 10:

FORMAT Y DECSTRING B2D

will leave zero in the first two bytes of DECSTRING, +9 in the next two bytes, 10 in the next byte and the ASCII characters “2345000000xxxxxxxxxx” thereafter (x = undefined). Vice versa, one can set up a decimal string in a 25 byte array according to these rules and call:

FORMAT DECSTRING Y D2B                  

which will leave the real number corresponding to DECSTRING in Y. The word DEC. (defined in listing 1) makes use of this conversion routine to output a real number.

Try and play with those floating point routines a little; they make a very useful addition to Forth 1.1, if you want to do any kind of numerical calculations. You may want to time the floating point package using the benchmarks at the end of listing 1. I found that an 80-bit precision add takes about 0.4 ms, a multiply about 1 ms.

In the next issue of MacTech we will take a closer look at toolbox calling from Forth and at the internal structure of Forth words, so that you can write in-line assembly code for time critical operations.

 

Community Search:
MacTech Search:

Software Updates via MacUpdate

Live Home 3D Pro 3.6.2 - $49.99
Live Home 3D Pro is powerful yet intuitive home design software that lets you build the house of your dreams right on your Mac, iPhone or iPad. It has every feature of Live Home 3D, plus some... Read more
RapidWeaver 8.2 - Create template-based...
RapidWeaver is a next-generation Web design application to help you easily create professional-looking Web sites in minutes. No knowledge of complex code is required, RapidWeaver will take care of... Read more
Opera 60.0.3255.109 - High-performance W...
Opera is a fast and secure browser trusted by millions of users. With the intuitive interface, Speed Dial and visual bookmarks for organizing favorite sites, news feature with fresh, relevant content... Read more
DEVONthink Pro 3.0beta2 - Knowledge base...
DEVONthink Pro is your essential assistant for today's world, where almost everything is digital. From shopping receipts to important research papers, your life often fills your hard drive in the... Read more
Tunnelblick 3.7.9 - GUI for OpenVPN.
Tunnelblick is a free, open source graphic user interface for OpenVPN on OS X. It provides easy control of OpenVPN client and/or server connections. It comes as a ready-to-use application with all... Read more
Carbon Copy Cloner 5.1.9 - Easy-to-use b...
Carbon Copy Cloner backups are better than ordinary backups. Suppose the unthinkable happens while you're under deadline to finish a project: your Mac is unresponsive and all you hear is an ominous,... Read more
Dropbox 73.4.118 - Cloud backup and sync...
Dropbox is an application that creates a special Finder folder that automatically syncs online and between your computers. It allows you to both backup files and keeps them up-to-date between systems... Read more
Postbox 6.1.18 - 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
Wireshark 3.0.2 - Network protocol analy...
Wireshark is one of the world's foremost network protocol analyzers, and is the standard in many parts of the industry. It is the continuation of a project that started in 1998. Hundreds of... Read more
BetterTouchTool 2.856 - Customize multi-...
BetterTouchTool adds many new, fully customizable gestures to the Magic Mouse, Multi-Touch MacBook trackpad, and Magic Trackpad. These gestures are customizable: Magic Mouse: Pinch in / out (zoom... Read more

AFK Arena guide - Everything you need to...
Ok, so if you're like me, you've been playing (and sometimes waiting) your way through AFK Arena, only to learn there's a lot more to it than there appears on the surface. There's guilds, a PvP arena, and all sorts of other systems and game modes... | Read more »
Explore an epic fantasy world in MMORPG...
Webzen have just announced the official launch date for its stunning MMORPG ‘MU Origin 2’ which will arrive for iOS and Android on May 28th. It will be the second spinoff from the classic PC-based MU Online, and it looks to further refine the... | Read more »
Solar Explorer: New Dawn guide - Tips an...
Solar Explorer: New Dawn is a lunar lander game that really ratchets the intensity up to 11. With all of the asteroids flying around as you fly around at seemingly breakneck speeds, it can be easy to feel overwhelmed bythe whole thing. | Read more »
The Dalaran Heist - How Hearthstone...
I am someone who wrote Hearthstone off a while ago. It was hard not to try and stick with it. The game has incredible production values and a core of really great talent working on the game continuously to keep it feeling fresh and fun (full... | Read more »
Steam Link App - Everything You Need to...
Steam Link has finally released for iOS! That’s right, you can play your epic backlog of PC games on the go now. Well… sort of. While the Steam Link app was announced seemingly ages ago, it only got actual approval for release last night. Check out... | Read more »
Pre-register now for endless superhero r...
Talking Tom Hero Dash is set to take the ever-popular Talking Tom and Friends franchise in a brand new direction as it opens pre-registration to players worldwide. Not only does it promise to be a beautifully rendered, fast-paced, action-packed... | Read more »
AFK Arena - Guild Wars guide
Ok, so if you're like me, you've been playing (and sometimes waiting) your way through AFK Arena, only to learn there's a lot more to it than there appears on the surface. There's guilds, a PvP arena, and all sorts of other systems and game modes... | Read more »
Superhero-themed Talking Tom Hero Dash i...
One of the exciting releases that we’re looking forward to is Talking Tom Hero Dash, an upcoming superhero-themed runner created by Outfit7. This new game is an action-packed endless runner that takes you on an epic adventure to assemble the... | Read more »
Kingdom Rush Vengeance Update Guide 2 -...
Kingdom Rush: Vengeance just got updated once again to add more content to the game. This addition, called The Frozen Nightmare, adds three new levels, five new enemies, two new heroes, and some new achievements. | Read more »
Save the world with SCIENCE in the upcom...
Previous versions of space colonization game TerraGenesis encouraged you to explore the galaxy and settle its planets. The eagerly-awaited 5.0 update will try to smash them to bits. Yep, with a new "world killers" setting, you can unleash... | Read more »

Price Scanner via MacPrices.net

12″ 1.2GHz MacBooks on sale for $999, $300 of...
Amazon has current-generation 12″ 1.2GHz Retina MacBooks on sale for $300 off Apple’s MSRP. Shipping is free: 12″ 1.2GHz Space Gray MacBook: $999.99 $300 off MSRP 12″ 1.2GHz Silver MacBook: $999.99 $... Read more
Here’s how to save $200 on Apple’s new 8-Core...
Apple has released details of their Education discount associated with the new 2019 15″ 6-Core and 8-Core MacBook Pros. Take $200 off the price of the new 8-Core model (now $2599) and $150 off the 15... Read more
Price drops! 2018 15″ 2.2GHz 6-Core MacBook P...
Amazon has dropped prices on clearance 2018 15″ 2.2GHz 6-Core Touch Bar MacBook Pros by $300 with models now available for $2099. These are the same models sold by Apple in their retail and online... Read more
Apple drops prices on 2018 13″ 2.3GHz Quad-Co...
Apple has dropped prices on Certified Refurbished 2018 13″ 2.3GHz 4-Core Touch Bar MacBook Pros with prices now starting at $1489. Apple’s one-year warranty is included, shipping is free, and each... Read more
Apple drops prices on 2018 Certified Refurbis...
Apple has dropped prices on clearance 2018 15″ 6-Core Touch Bar MacBook Pro, Certified Refurbished, with models available starting at only $1999. Each model features a new outer case, shipping is... Read more
Price drops! Clearance 2018 13″ Quad Core Mac...
Amazon has dropped prices on 2018 13″ Apple Quad-Core MacBook Pros with models now available for $250 off original MSRP. Shipping is free. Select Amazon as the seller, rather than a third-party, to... Read more
How Much Is ‘Solace’ Of Mind Worth When Buyin...
COMMENTARY: 05.22.19- Smartphone cases give us peace of mind by providing ample protection for such a fragile gadget and the sky’s the limit as far as choices go with a plethora of brands, styles,... Read more
Get a 13″ Touch Bar MacBook Pro for the lowes...
Apple has Certified Refurbished 2017 13″ 3.1GHz Dual-Core i5 Touch Bar MacBook Pros available starting at $1439, ranging up to $390 off original MSRP. Each MacBook features a new outer case, shipping... Read more
Apple adds new 15″ 8-Core MacBook Pro to line...
Apple has added a new 15″ MacBook Pro to its lineup featuring a 9th generation 2.3GHz 8-Core Intel i9 processor, 16GB of RAM, a 512GB SSD, and a Radeon Pro 560X with 4GB of GDDR5 memory for $2799.... Read more
21″ 2.3GHz iMac available for $999 at B&H...
B&H Photo has the 2018 21″ 2.3GHz Apple iMac on sale for $100 off MSRP. This is the same model offering by Apple in their retail and online stores. Shipping is free: – 21″ 2.3GHz iMac (MMQA2LL/A... Read more

Jobs Board

Best Buy *Apple* Computing Master - Best Bu...
**690427BR** **Job Title:** Best Buy Apple Computing Master **Job Category:** Sales **Location Number:** 000860-Charlottesville-Store **Job Description:** **What Read more
*Apple* Mobile Master - Best Buy (United Sta...
**696430BR** **Job Title:** Apple Mobile Master **Job Category:** Store Associates **Location Number:** 001012-Bismarck-Store **Job Description:** **What does a Best Read more
Manager - *Apple* Team - SHI International...
…opportunity available in the Hardware & Advanced Solutions Department as the Manager of the Apple Team The Manager must be familiar with all aspects of Apple Read more
Best Buy *Apple* Computing Master - Best Bu...
**696375BR** **Job Title:** Best Buy Apple Computing Master **Job Category:** Sales **Location Number:** 000203-North Austin-Store **Job Description:** **What does a Read more
Geek Squad *Apple* Master Consultation Agen...
**696286BR** **Job Title:** Geek Squad Apple Master Consultation Agent **Job Category:** Services/Installation/Repair **Location Number:** 000172-Rivergate-Store Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.