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.

 
AAPL
$100.75
Apple Inc.
+0.64
MSFT
$46.36
Microsoft Corpora
-0.08
GOOG
$577.36
Google Inc.
+1.00

MacTech Search:
Community Search:

Software Updates via MacUpdate

QuickBooks 2015 16.0.0.1352 R1 - Financi...
QuickBooks 2015 helps you manage your business easily and efficiently. Organize your finances all in one place, track money going in and out of your business, and spot areas where you can save.... Read more
Mac DVDRipper Pro 5.0.1 - Copy, backup,...
Mac DVDRipper Pro is the DVD backup solution that lets you protect your DVDs from scratches, save your batteries by reading your movies from your hard disk, manage your collection with just a few... Read more
Apple OS X bash Update 1.0 - Fix for sec...
The OS X bash Update fixes a security flaw in the bash UNIX shell on OS X 10.9.5 (also on OS X 10.8 and 10.7 [see Related Links below]). OS X 10.9.5 or later Downloads for OS X 10.8 and OS X 10.7 in... Read more
SyncTwoFolders 2.0.5 - Syncs two user-sp...
SyncTwoFolders simply synchronizes two folders. It supports synchronization across mounted network drives and it is a possibility to run a simulation showing in a log what will be done. Please visit... Read more
FinderPop 2.5.7 - Classic Mac utility, n...
FinderPop is a Universal preference pane that extends OS X's contextual menus using a FinderPop Items folder much as the Apple Menu Items folder used to do for the Apple menu. It has other features... Read more
VueScan 9.4.45 - 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
LibreOffice 4.3.2.2 - Free Open Source o...
LibreOffice is an office suite (word processor, spreadsheet, presentations, drawing tool) compatible with other major office suites. The Document Foundation is coordinating development and... Read more
calibre 2.4 - Complete e-library managem...
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... Read more
Default Folder X 4.6.9b1 - Enhances Open...
Default Folder X attaches a toolbar to the right side of the Open and Save dialogs in any OS X-native application. The toolbar gives you fast access to various folders and commands. You just click... Read more
Beamer 2.0.4 - Stream any movie file fro...
Beamer streams to your Apple TV.... Plays any movie file - Just like the popular desktop movie players, Beamer accepts all common formats, codecs and resolutions. AVI, MKV, MOV, MP4, WMV, FLV. To... Read more

Latest Forum Discussions

See All

WW2: Sandbox. Strategy & Tactics (G...
WW2: Sandbox. Strategy & Tactics 1.0.0 Device: iOS Universal Category: Games Price: $9.99, Version: 1.0.0 (iTunes) Description: Sandbox is the unlimited sequel to our Strategy & Tactics: World War II. We've abandoned... | Read more »
apeFilter (Music)
apeFilter 1.0 Device: iOS Universal Category: Music Price: $6.99, Version: 1.0 (iTunes) Description: | Read more »
Shred It! Review
Shred It! Review By Jennifer Allen on September 30th, 2014 Our Rating: :: GORGEOUS BUT BASICUniversal App - Designed for iPhone and iPad It might look lovely, but Shred It! is a pretty shallow endless runner/snowboarding game.   | Read more »
It Came From Canada: Angry Birds: Transf...
Anyone afraid that throwing Transformers into the Angry Birds mix would result in a Michael Bay-level of childhood pillaging can rest easy. While Rovio’s famous fowls may be a 21st century staple, Angry Birds: Transformers wears its affection for... | Read more »
Galaxy Trucker Review
Galaxy Trucker Review By Rob Thomas on September 30th, 2014 Our Rating: :: IN FOR THE LONG HAULiPad Only App - Designed for the iPad We got a great big convoy, rockin’ through the night… the endless night of outer space, that is.... | Read more »
Moon and Sun – children’s book Review
Moon and Sun – children’s book Review By Amy Solomon on September 30th, 2014 Our Rating: Moon and Sun is a fable-like children’s book with lush illustrations.   Developer: Marcio Monteiro Price: $3.99 Version: 1.0 App Reviewed on... | Read more »
Kairosoft Finally Brings The Pyraplex to...
Kairosoft Finally Brings The Pyraplex to iOS Posted by Jessica Fisher on September 30th, 2014 [ permalink ] Universal App - Designed for iPhone and iPad | Read more »
Yeti’s Parole Officer Review
Yeti’s Parole Officer Review By Jennifer Allen on September 30th, 2014 Our Rating: Universal App - Designed for iPhone and iPad Yeti’s Parole Officer proves that looks aren’t everything in this entertaining, if plain, piece of... | Read more »
Record Keeper and World Wide Words – Two...
Record Keeper and World Wide Words – Two New Final Fantasy Games Arrive on iOS in Japan Posted by Ellis Spice on September 30th, 2014 [ permalink ] | Read more »
iPollute Review
iPollute Review By Nadia Oxford on September 30th, 2014 Our Rating: :: iPOLLUTE, uPOLLUTEUniversal App - Designed for iPhone and iPad iPollute is a delightful-looking pollution simulator, though it’s a bit light on “game” content... | Read more »

Price Scanner via MacPrices.net

Apple Boycotts German Magazine Computer Bild...
Apple has revoked its PR accreditation of Germany’s Computer Bild, Europe’s best-selling PC magazine, in reaction to Bild’s posting of a “#Bentgate” YouTube video. Axel Telzerow, editor in chief of... Read more
iPhone 6 & iPhone 6 Plus Available in Chi...
Apple has announced that iPhone 6 and iPhone 6 Plus will be available in China beginning Friday, October 17 from the Apple Online Store (http://www.apple.com), Apple’s retail stores, and an expansive... Read more
MacBook Airs on sale for $100 off MSRP, start...
Best Buy has the new 2014 MacBook Airs on sale for $100 off MSRP on their online store. Choose free home shipping or free local store pickup (if available). Prices valid for online orders only, in-... Read more
Apple Releases OS X Mavericks bash Update 1.0...
Apple has released a patch update for OS X Mavericks users to address the recently-detected “Shellshock” security bug in BSD UNIX’s bash shell. Apple says only a few Mac users who had manually... Read more
Pivotal Payments Ready for Apple Pay – FlexPo...
Pivotal Payments, a provider of merchant services and global payment processing solutions, has announced its proprietary FlexPoint platform will support credit and debit transactions through Apple’s... Read more
iStabilizer Announces Tabarm — First Friction...
iStabilizer, a specialist in universal lightweight compact tripods, steady cams, dollies, mounts, and remotes for smartphones, tablets, and cameras, announced today the iStabilizer tabArm, the first... Read more
IStabilizer Flex Smartphone Tripod Wins Usa T...
iStabilizer, a specialist in universal lightweight compact tripods, steady cams, and other products for smartphones, tablets, and cameras, has announced today that its iStabilizer Flex smartphone... Read more
13-inch 2.8GHz Retina MacBook Pro on sale for...
B&H Photo has the new 2014 13″ 2.8GHz Retina MacBook Pro on sale for $1699.99 including free shipping plus NY sales tax only. They’ll also include free copies of Parallels Desktop and LoJack for... Read more
15-inch Retina MacBook Pros on sale for up to...
B&H Photo has the new 2014 15″ Retina MacBook Pros on sale for up to $150 off MSRP. Shipping is free, and B&H charges NY sales tax only. They’ll also include free copies of Parallels Desktop... Read more
Get Down to Business On Your iPad With Free N...
Utah based Poem LLC has introduced Nexticy 1.0, a full-featured, affordable (Free) forms application for iPad. Nexticy makes it ‘way easy’ to create, store, retrieve and analyze paper-like forms of... Read more

Jobs Board

*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* Retail - Multiple Positions (US) - A...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
Senior Event Manager, *Apple* Retail Market...
…This senior level position is responsible for leading and imagining the Apple Retail Team's global event strategy. Delivering an overarching brand story; in-store, Read more
*Apple* Solutions Consultant (ASC) - Apple (...
**Job Summary** The ASC is an Apple employee who serves as an Apple brand ambassador and influencer in a Reseller's store. The ASC's role is to grow Apple Read more
Project Manager / Business Analyst, WW *Appl...
…a senior project manager / business analyst to work within our Worldwide Apple Fulfillment Operations and the Business Process Re-engineering team. This role will work Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.