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

jAlbum Pro 12.6.4 - Organize your digita...
jAlbum Pro has all the features you love in jAlbum, but comes with a commercial license. With jAlbum, you can create gorgeous custom photo galleries for the Web without writing a line of code!... Read more
jAlbum 12.6.4 - Create custom photo gall...
With jAlbum, you can create gorgeous custom photo galleries for the Web without writing a line of code! Beginner-friendly, with pro results Simply drag and drop photos into groups, choose a design... Read more
Microsoft Remote Desktop 8.0.16 - Connec...
With Microsoft Remote Desktop, you can connect to a remote PC and your work resources from almost anywhere. Experience the power of Windows with RemoteFX in a Remote Desktop client designed to help... Read more
Spotify 1.0.4.90. - Stream music, create...
Spotify is a streaming music service that gives you on-demand access to millions of songs. Whether you like driving rock, silky R&B, or grandiose classical music, Spotify's massive catalogue puts... Read more
djay Pro 1.1 - Transform your Mac into a...
djay Pro provides a complete toolkit for performing DJs. Its unique modern interface is built around a sophisticated integration with iTunes and Spotify, giving you instant access to millions of... Read more
Vivaldi 1.0.118.19 - Lightweight browser...
Vivaldi browser. In 1994, two programmers started working on a web browser. Our idea was to make a really fast browser, capable of running on limited hardware, keeping in mind that users are... Read more
Stacks 2.6.11 - New way to create pages...
Stacks is a new way to create pages in RapidWeaver. It's a plugin designed to combine drag-and-drop simplicity with the power of fluid layout. Features: Fluid Layout: Stacks lets you build pages... Read more
xScope 4.1.3 - Onscreen graphic measurem...
xScope is powerful set of tools that are ideal for measuring, inspecting, and testing on-screen graphics and layouts. Its tools float above your desktop windows and can be accessed via a toolbar,... Read more
Cyberduck 4.7 - FTP and SFTP browser. (F...
Cyberduck is a robust FTP/FTP-TLS/SFTP browser for the Mac whose lack of visual clutter and cleverly intuitive features make it easy to use. Support for external editors and system technologies such... Read more
Labels & Addresses 1.7 - Powerful la...
Labels & Addresses is a home and office tool for printing all sorts of labels, envelopes, inventory labels, and price tags. Merge-printing capability makes the program a great tool for holiday... Read more

Discover Your Reflexes With Minimalist G...
Discover O, BYOF Studios, may look simple at first with its' color matching premise and swipe controls, but as you speed up the task becomes more daunting. [Read more] | Read more »
Here's Another Roundup of Notable A...
Now that the Apple Watch is publically available (kind of), even more apps and games have been popping up for it. Some of them are updates to existing software, others are brand new. The main thing is that they're all for the Apple Watch, and if you... | Read more »
Use Batting Average and the Apple Watch...
Batting Average, by Pixolini, is designed to help you manage your statistics. Every time you go to bat, you can use your Apple Watch to track  your swings, strikes, and hits. [Read more] | Read more »
Celebrate Studio Pango's 3rd Annive...
It is time to party, Pangoland pals! Studio Pango is celebrating their 3rd birthday and their gift to you is a new update to Pangoland. [Read more] | Read more »
Become the World's Most Important D...
Must Deliver, by cherrypick games, is a top-down endless-runner witha healthy dose of the living dead. [Read more] | Read more »
SoundHound + LiveLyrics is Making its De...
SoundHound Inc. has announced that SoundHound + LiveLyrics, will be one of the first third-party apps to hit the Apple Watch. With  SoundHound you'll be able to tap on your watch and have the app recognize the music you are listening to, then have... | Read more »
Adobe Joins the Apple Watch Lineup With...
A whole tidal wave of apps are headed for the Apple Watch, and Adobe has joined in with 3 new ways to enhance your creativity and collaborate with others. The watch apps pair with iPad/iPhone apps to give you total control over your Adobe projects... | Read more »
Z Steel Soldiers, Sequel to Kavcom'...
Kavcom has released Z Steel Soldiers, which continues the story of the comedic RTS originally created by the Bitmap Brothers. [Read more] | Read more »
Seene Lets You Create 3D Images With You...
Seene, by Obvious Engineering, is a 3D capture app that's meant to allow you to create visually stunning 3D images with a tap of your finger, and then share them as a 3D photo, video or gif. [Read more] | Read more »
Lost Within - Tips, Tricks, and Strategi...
Have you just downloaded Lost Within and are you in need of a guiding hand? While it’s not the toughest of games out there you might still want some helpful tips to get you started. [Read more] | Read more »

Price Scanner via MacPrices.net

Zoho Business Apps for Apple Watch Put Select...
Pleasanton, California based Zoho has launched Zoho Business Apps for Apple Watch, a line of apps that extends Zoho business applications to let users perform select functions from an Apple Watch.... Read more
Universal Stylus Initiative Launched to Creat...
OEMs, stylus and touch controller manufacturers have announced the launch of Universal Stylus Initiative (USI), a new organization formed to develop and promote an industry specification for an... Read more
Amazon Shopping App for Apple Watch
With the new Amazon shopping app for Apple Watch, Amazon customers with one of the wearable devices can simply tap the app on the watch to purchase items in seconds, or save an idea for later. The... Read more
Intel Compute Stick: A New Mini-Computing For...
The Intel Compute Stick, a new pocket-sized computer based on a quad-core Intel Atom processor running Windows 8.1 with Bing, is available now through Intel Authorized Dealers across much of the... Read more
Heal to Launch First One-Touch House Call Doc...
Santa Monica, California based Heal, a pioneer in on-demand personal health care services — will offer the first one-touch, on-demand house call doctor app for the Apple Watch. Heal’s Watch app,... Read more
Mac Notebooks: Avoiding MagSafe Power Adapter...
Apple Support says proper usage, care, and maintenance of Your Mac notebook’s MagSafe power adapter can substantially increase the the adapter’s service life. Of course, MagSafe itself is an Apple... Read more
12″ Retina MacBook In Shootout With Air And P...
BareFeats’ rob-ART morgan has posted another comparison of the 12″ MacBook with other Mac laptops, noting that the general goodness of all Mac laptops can make which one to purchase a tough decision... Read more
FileMaker Go for iPad and iPhone: Over 1.5 Mi...
FileMaker has announced that its FileMaker Go for iPad and iPhone app has surpassed 1.5 million downloads from the iTunes App Store. The milestone confirms the continued popularity of the FileMaker... Read more
Sale! 13-inch 2.7GHz Retina MacBook Pro for $...
 Best Buy has the new 2015 13″ 2.7GHz/128GB Retina MacBook Pro on sale for $1099 – $200 off MSRP. Choose free shipping or free local store pickup (if available). Price for online orders only, in-... Read more
Minimalist MacBook Confirms Death of Steve Jo...
ReadWrite’s Adriana Lee has posted a eulogy for the “Digital Hub” concept Steve Jobs first proposed back in 2001, declaring the new 12-inch MacBook with its single, over-subscribed USB-C port to be... Read more

Jobs Board

*Apple* Client Systems Solution Specialist -...
…drive revenue and profit in assigned sales segment and/or region specific to the Apple brand and product sets. This person will work directly with CDW Account Managers Read more
*Apple* Retail - Multiple Positions (US) - A...
Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, you're also the Read more
*Apple* Support Technician IV - Jack Henry a...
Job Description Jack Henry & Associates is seeking an Apple Support Technician. This position while acting independently, ensures the proper day-to-day control of Read more
*Apple* Client Systems Solution Specialist -...
…drive revenue and profit in assigned sales segment and/or region specific to the Apple brand and product sets. This person will work directly with CDW Account Managers Read more
*Apple* Software Support - Casper (Can work...
…experience . Full knowledge of Mac OS X and prior . Mac OSX / Server . Apple Remote Desktop . Process Documentation . Ability to prioritize multiple tasks in a fast pace Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.