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

EtreCheck 3.1.5 - For troubleshooting yo...
EtreCheck is an app that displays the important details of your system configuration and allow you to copy that information to the Clipboard. It is meant to be used with Apple Support Communities to... Read more
WALTR 2 2.0.8 - $39.95
WALTR 2 helps you wirelessly drag-and-drop any music, ringtones, videos, PDF, and ePub files onto your iPhone, iPad, or iPod without iTunes. It is the second major version of Softorino's critically-... Read more
Carbon Copy Cloner 4.1.12 - Easy-to-use...
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 16.3.27 - Cloud backup and synch...
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 keep them up-to-date between systems... Read more
Microsoft OneNote 15.29 - Free digital n...
OneNote is your very own digital notebook. With OneNote, you can capture that flash of genius, that moment of inspiration, or that list of errands that's too important to forget. Whether you're at... Read more
Spotify 1.0.44.100. - Stream music, crea...
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
SpamSieve 2.9.27 - Robust spam filter fo...
SpamSieve is a robust spam filter for major email clients that uses powerful Bayesian spam filtering. SpamSieve understands what your spam looks like in order to block it all, but also learns what... Read more
VueScan 9.5.62 - Scanner software with a...
VueScan is a scanning program that works with most high-quality flatbed and film scanners to produce scans that have excellent color fidelity and color balance. VueScan is easy to use, and has... Read more
Fantastical 2.3.2 - Create calendar even...
Fantastical 2 is the Mac calendar you'll actually enjoy using. Creating an event with Fantastical is quick, easy, and fun: Open Fantastical with a single click or keystroke Type in your event... Read more
PCalc 4.4.4 - Full-featured scientific c...
PCalc is a full-featured, scriptable scientific calculator with support for hexadecimal, octal, and binary calculations, as well as an RPN mode, programmable functions, and an extensive set of unit... Read more

Latest Forum Discussions

See All

Track Santa with these three festive app...
Christmas is fast approaching and that means it's time to prepare for Santa's yearly pilgrimage around the globe. Christmas Eve is an exciting time as parents help their kids get ready to welcome Santa. You've got the cookies and milk all planned... | Read more »
Galaxy on Fire 3 and four other fantasti...
Galaxy on Fire 3 - Manticore brings the series back for another round of daring space battles. It's familiar territory for folks who are familiar with the franchise. If you've beaten the game and are looking to broaden your horizons, might we... | Read more »
The best apps for your holiday gift exch...
What's that, you say? You still haven't started your holiday shopping? Don't beat yourself up over it -- a lot of people have been putting it off, too. It's become easier and easier to procrastinate gift shopping thanks to a number of apps that... | Read more »
Toca Hair Salon 3 (Education)
Toca Hair Salon 3 1.0 Device: iOS Universal Category: Education Price: $2.99, Version: 1.0 (iTunes) Description: | Read more »
Winter comes to Darkwood as Seekers Note...
MyTona, based in the chilly Siberian city of Yakutsk, has brought a little festive fun to its hidden object game Seekers Notes: Hidden Mystery. The Christmas update introduces some new inhabitants to players, and with them a chance to win plenty of... | Read more »
Bully: Anniversary Edition (Games)
Bully: Anniversary Edition 1.03.1 Device: iOS Universal Category: Games Price: $6.99, Version: 1.03.1 (iTunes) Description: *** PLEASE NOTE: This game is officially supported on the following devices: iPhone 5 and newer, iPod Touch... | Read more »
PINE GROVE (Games)
PINE GROVE 1.0 Device: iOS Universal Category: Games Price: $1.99, Version: 1.0 (iTunes) Description: A pine grove where there are no footsteps of people due to continuous missing cases. The case is still unsolved and nothing has... | Read more »
Niantic teases new Pokémon announcement...
After rumors started swirling yesterday, it turns out there is an official Pokémon GO update on its way. We’ll find out what’s in store for us and our growing Pokémon collections tomorrow during the Starbucks event, but Niantic will be revealing... | Read more »
3 reasons why Nicki Minaj: The Empire is...
Nicki Minaj is as business-savvy as she is musically talented and she’s proved that by launching her own game. Designed by Glu, purveyors of other fine celebrity games like cult favorite Kim Kardashian: Hollywood, Nicki Minaj: The Empire launched... | Read more »
Clash of Clans is getting its own animat...
Riding on its unending wave of fame and success, Clash of Clans is getting an animated web series based on its Clash-A-Rama animated shorts.As opposed to the current shorts' 60 second run time, the new and improved Clash-A-Rama will be comprised of... | Read more »

Price Scanner via MacPrices.net

Never Settle for Low Performing Wifi With iOS...
AppYogi Software has announced the release of WiFi Signal Strength Status App 1.0, the company’s new utility developed exclusively for macOS. WiFi Signal Strength Status App features a unique, single... Read more
New 2016 13-inch Touch Bar MacBook Pros in st...
B&H Photo has stock of new 2016 Apple 13″ Touch Bar MacBook Pro models, each including free shipping plus NY sales tax only: - 13″ 2.9GHz/512GB Touch Bar MacBook Pro Space Gray: $1999 - 13″ 2.... Read more
New 2016 15″ Touch Bar MacBook Pros in stock...
B&H Photo has new 2016 Apple 15″ Touch Bar MacBook Pro models in stock today including free shipping plus NY sales tax only: - 15″ 2.7GHz Touch Bar MacBook Pro Space Gray: $2799 - 15″ 2.7GHz... Read more
DietSensor App Targeting Diabetes and Obesity...
DietSensor, Inc., a developer of smart food and nutrition applications designed to fight diabetes and obesity and help improve overall fitness, has announced the launch of its DietSensor app for... Read more
Holiday 2016 13-inch 2.0GHz MacBook Pro sales...
B&H has the non-Touch Bar 13″ MacBook Pros in stock today for $50-$100 off MSRP. Shipping is free, and B&H charges NY sales tax only: - 13″ 2.0GHz MacBook Pro Space Gray (MLL42LL/A): $1449 $... Read more
Holiday sale: Apple TVs for $51-$40 off MSRP,...
Best Buy has dropped their price on the 64GB Apple TV to $159.99 including free shipping. That’s $40 off MSRP. 32GB Apple TVs are on sale right now for $98 on Sams Club’s online store. That’s $51 off... Read more
12-inch Retina MacBooks, Apple refurbished, n...
Apple has restocked a full line of Certified Refurbished 2016 12″ Retina MacBooks, now available for $200-$260 off MSRP. Refurbished 2015 models are available starting at $929. Apple will include a... Read more
Holiday sale: 12-inch Retina MacBook for $100...
B&H has 12″ Retina MacBooks on sale for $100 off MSRP as part of their Holiday sale. Shipping is free, and B&H charges NY sales tax only: - 12″ 1.1GHz Space Gray Retina MacBook: $1199 $100... Read more
Apple refurbished 13-inch MacBook Airs availa...
Apple has Certified Refurbished 13″ MacBook Airs available starting at $849. An Apple one-year warranty is included with each MacBook, and shipping is free: - 13″ 1.6GHz/8GB/128GB MacBook Air: $849 $... Read more
Apple refurbished iMacs available for up to $...
Apple has Certified Refurbished 2015 21″ & 27″ iMacs available for up to $350 off MSRP. Apple’s one-year warranty is standard, and shipping is free. The following models are available: - 21″ 3.... Read more

Jobs Board

*Apple* Retail - Multiple Positions - Apple,...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
US- *Apple* Store Leader Program - Apple (Un...
…Summary Learn and grow as you explore the art of leadership at the Apple Store. You'll master our retail business inside and out through training, hands-on Read more
Automotive Detailer - *Apple* Used Autos -...
We are currently conductinginterviews and will be accepting applications for a part-time detailer. Apple Used Autos is a great place to work andstart a career. We Read more
*Apple* Retail - Multiple Positions - Apple,...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
*Apple* Retail - Multiple Positions- Trumbul...
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
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.