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

How to build a successful civilisation i...
GodFinger 2 grants you godlike powers, leaving you to raise a civilization of followers. In the spirit of games like Black & White, the GodFinger games will see you building bigger and better villages, developing more advanced technology and... | Read more »
How to get all the crabs in Mr Crab 2
Mr. Crab 2 may look like a cutesy platformer for kids, but if you're the kind of person who likes to complete a game 100%, you'll soon realise that it's a tougher than a crustacean's shell. [Read more] | Read more »
How to be a star in Britney Spears: Amer...
If you've ever wanted to be a star, baby, then you've probably already checked out Britney Spears: American Dream and are happily making your way up the charts. But fame doesn't come easy, and everyone needs a helping hand sometimes. So we've got... | Read more »
AppSpy is hiring a part time Staff Write...
| Read more »
How to save lives in ER Surgery Simulato...
A serious earthquake has struck a nearby town in ER Surgery Simulator - Emergency Doctor, and it’s up to you to save the victims. [Read more] | Read more »
Tips and tricks to get a high score in G...
Ketchapp Games loves the endless runner genre. And its newest game, Gravity Switch, is no exception. Gravity Switch takes a fresh approach, though, as you move a block, suspended in zero gravity, safely through a maze of shifting pillars. If the... | Read more »
Tips and tricks to get a high score in S...
Smash Fu is a high-paced tile-tapping game that requires quick reflexes and some practice. You’ll have to smash bricks with the skill of a seasoned black belt to get a high score. To raise the stakes a bit, you’ll also have to avoid tapping any... | Read more »
How to keep the ball rolling in Dropple
If you're new to the minimalist puzzler Dropple, you may find yourself struggling to make it beyond the first couple of steps before your ball falls into the endless abyss below. [Read more] | Read more »
Game Craft releases new Legend of War ti...
Set for release at the end of this month, real time strategy title Legend of War seems sure to delight with a veritable feast of sweet features to get stuck into. Developed by Game Craft, the game is due for release through both the App Store and... | Read more »
How not to die in Traffic Rider
Traffic Rider, an Out Run-esque game in which your ride a motorcycle recklessly into trffic, might not seem particularly complicated. [Read more] | Read more »

Price Scanner via MacPrices.net

Textkraft Professional Becomes A Mobile Produ...
The new update 4.1 of Textkraft Professional for the iPad comes with many new and updated features that will be particularly of interest to self-publishers of e-books. Highlights include import and... Read more
SnipNotes 2.0 – Intelligent note-taking for i...
Indie software developer Felix Lisczyk has announced the release and immediate availability of SnipNotes 2.0, the next major version of his productivity app for iOS devices and Apple Watch.... Read more
Pitch Clock – The Entrepreneur’s Wingman Laun...
Grand Rapids, Michigan based Skunk Tank has announced the release and immediate availability of Pitch Clock – The Entrepreneur’s Wingman 1.1, the company’s new business app available exclusively on... Read more
13-inch 2.9GHz Retina MacBook Pro on sale for...
B&H Photo has the 13″ 2.9GHz Retina MacBook Pro (model #MF841LL/A) on sale for $1599 including free shipping plus NY tax only. Their price is $200 off MSRP. Amazon also has the 13″ 3.9GHz Retina... Read more
Apple price trackers, updated continuously
Scan our Apple Price Trackers for the latest information on sales, bundles, and availability on systems from Apple’s authorized internet/catalog resellers. We update the trackers continuously: - 15″... Read more
Clearance 12-inch Retina MacBooks available s...
B&H Photo has dropped prices on leftover 2015 12″ Retina MacBooks with models now available starting at $999. Shipping is free, and B&H charges NY tax only: - 12″ 1.1GHz Gray Retina MacBook... Read more
Check Apple prices on any device with the iTr...
MacPrices is proud to offer readers a free iOS app (iPhones, iPads, & iPod touch) and Android app (Google Play and Amazon App Store) called iTracx, which allows you to glance at today’s lowest... Read more
New 2016 13-inch 256GB MacBook Air on sale fo...
B&H Photo has the new 13″ 1.6GHz/256GB MacBook Air (model MMGG2LL/A) on sale for $1149 including free shipping plus NY sales tax only. Their price is $50 off MSRP. Amazon has the 13″ 1.6GHz/256GB... Read more
Apple refurbished iPad Air 2s available start...
Apple has Certified Refurbished iPad Air 2 available starting at $339. Apple’s one-year warranty is included with each model, and shipping is free: - 128GB Wi-Fi iPad Air 2: $499 - 64GB Wi-Fi iPad... Read more
Accenture and Vatican Opera Romana Pellegrina...
Accenture has announced that the official mobile application for the Extraordinary Jubilee Year of Mercy declared by Pope Francis has been built and launched by Accenture Mobility, part of Accenture... Read more

Jobs Board

*Apple* Nissan Service Technicians - Apple A...
Apple Automotive is one of the fastest growing dealer...and it shows. Consider making the switch to the Apple Automotive Group today! At Apple Automotive , Read more
ISCS *Apple* ID Site Support Engineer - APP...
…position, we are looking for an individual who has experience supporting customers with Apple ID issues and enjoys this area of support. This person should be Read more
Automotive Sales Consultant - Apple Ford Linc...
…you. The best candidates are smart, technologically savvy and are customer focused. Apple Ford Lincoln Apple Valley is different, because: $30,000 annual salary Read more
*Apple* Support Technician II - Worldventure...
…global, fast growing member based travel company, is currently sourcing for an Apple Support Technician II to be based in our Plano headquarters. WorldVentures is Read more
Restaurant Manager (Neighborhood Captain) - A...
…in every aspect of daily operation. WHY YOU'LL LIKE IT: You'll be the Big Apple . You'll solve problems. You'll get to show your ability to handle the stress and Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.