Floating Point Engine (FPE)
©Copyright 1989-91, Innovative Systems for all nontextual material, graphics. Figures, photographs, and all
computer program listings or code in any form, including object and source code. All rights reserved.
Innovative Systems, the Systems People, iS, Floating Point Engine, and FPE are trademarks of Innovative
Apple, Apple II, Apple //e, Apple AGS, DGS, ProDOS. and Macintosh are trademarks of Apple Computer, Inc.
SANE is a trademark of Apple Computer, Inc.
AppleWorks is a trademark of Apple Computer. Inc. licensed to Claris Corp.
ORCA/M, ORCA/C, and ORC A/Pascal are trademarks of The Byte Works, Inc.
TML BASIC and TML Pascal are trademarks of TML Systems, Inc.
Lisa816 Software is a copyright of Randall Hyde and HAL Labs.
Merlin 8/16 and Merlin 16+ are trademarks of Roger Wagner Publishing, Inc.
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If you discover physical defects in the manuals distributed with an Innovative Systems product or in the media
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Innovative Systems provides a Floating Point Engine card that is for installation in your personal computer.
Thus, the FPE is classified as a subassembly by the FCC. See instructions if interference to radio or television
reception is suspected.
Information to Users
This floating point card generates and uses radio frequency energy and if not installed and used properly - that
is, in strict accordance with the manufacturer's instructions - may cause interference to radio and television
If this card does cause interference to radio or television reception - which can be determined by turning the
equipment on and off and noting the effect of the power surge on the radio or television - you are encouraged to
try to correct the interference by one or more of the following measures:
• Reorient the receiving antenna.
• Move the computer away from the receive.
■ Plug the computer into a different oudet so that the computer and receiver are on different branch
If necessary you should consult with Innovative Systems or an experienced radio/television technician for
additional suggestions. You may find the following booklet prepared by the FCC helpful: "How to Identify and
Resolve Radio-TV Interference Problems." This booklet is available from the U.S. Government Printing
Office, Washington, DC, 20403, Stock No, 004-000-00345.4.
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TABLE OF CONTENTS
1. Introducing the Floating Point Engine 1
2. Instslliii the FPE*»*»n* i,«t 4 i liintiitifiiiiMUMit iiiaiiHtiitiini it,»iitti4«Miiit<tt 2>
2.2. Software 2
2.3. Slot Enabling on the Apple 1IGS 3
2.4. Slot Enabling on the Apple II, II+, and//e , 3
3. Access to the FPE 4
4. Interfacing to SANE. 6
4.1 Apple IIGS 6
4.2 Apple II, II+, and //e, 6
4.3 AppleWorks™ Classic
4.2 AppleWorks™ GS 6
5. How the FPE Transfers Data. 7
5.1 MEMREG and REGMEM Operations 7
5.2 REGREG Operations 8
5.3 Checking Status 9
6. Construction of an MC6888 I/MC68882 Command 1 1
7. Macro Usage 15
8 ■ /^k-t^OLlt tit 6 Mi ^^68 3 8 1 IlTltl S J^^^E <• .i<>i>>-»> '•••HMtt>i««*ll»i<tt(tilMl<iiiill >»lftlt«*t>l*lHl4ff**tlilllMHt*»l«Ml«l 17
9. Programming Hints 19
10. FPE Data and Register Formats 20
Innovative Systems Page i
1. Introducing the Floating Point Engine 1
The Innovative Systems™ (iS™) Floating Point Engine™ (FPE™) provides the most efficient floating point
math capability for all members of the Apple IF* family. Based on the Motorola MC6888 1 floating point
processor, the FPE brings a new dimension in computing power to the Apple II. The MC6888 1 is the same
floating point processor used with the Motorola 68000 microprocessor. Although you may need not be
concerned with specific capabilities of the FPE, software and programmers have access to:
* Eight general purpose, 80-bit floating-point data registers.
* Forty-six instructions, including 35 arithmetic operations.
* Full ANSI-IEEE 754-1985 floating point standard.
* Enhanced functions, including a complete set of trigonometric and transcendental functions.
* Seven data formats: byte, word, and long word integers; single, double, and extended precision real
numbers; and packed binary coded decimal string real numbers.
* Twenty-two constants including pi, e, and powers of 10.
* Concurrent instruction execution with the Apple II.
The FPE may be called in several ways. If the system software automatically loads all tools from your disk,
then the FPE is directiy callable from the Apple IIGS™ Standard Apple Numerics Environment (SANE™)
toolset. You need only boot the FPETOOLS disk to install the FPE software called FPETOOL.tNlT onto your
system disk in the /SYSTEM/SYSTEM. SETUP directory. All calls intended for SANE automatically call the
FPE once the system is rebooted from a complete shutdown. Thus, the FPE is transparent to you, except in
terms of speed improvement. This technique works only with the GS series.
For those users who have Apple II, 11+ , or //e computers, the FPETOOLS disk contains a version of 8-bit SANE
which addresses the FPE. This version of SANE replaces all calls except those calls to the Scanner and
Formatter operations (FPSTR2DEC, FCSTR2DEC, and FDEC2STR). For further information, refer to Section
For higher performance the FPE may be directly addressed through software by writing directly to the command
or reading directly from the status registers, as appropriate, in normal slot space (SCOnx, where n=8 plus the slot
number). This technique works equally well with any Apple II, DOS 3.2, DOS 3.3, ProDOS 8™, ProDOS 16,
and GS/OS™ without the overhead of using a toolset Please refer to Chapters 3 and 5.
The FPE is also compatible with all versions of AppleWorks Classic. You need only boot the FPETOOLS
installation disk to install FPE software software patches to AppleWorks. These patches will provide a
significant improvement in the calculation and recalculation time required by the spreadsheet and some database
This manual describes how to communicate with the Innovative Systems FPE. It does not explain the inner
workings of the Motorola MC6888 1 floating point coprocessor. Refer to the Motorola "MC68881/MC68882
Floating Point Coprocessor User's Manual", and related application notes, for details on how to use the
MC6888 1. These items are available from Motorola or, for a nominal charge, from Innovative Systems.
This manual is written to address different levels of users. If you do not plan to write your own code, you need
to read Chapters 1 and 2 only. If you intend to address the FPE using your own code, you will also need to read
and to understand Chapters 3 through 10.
2. Installing the FPE.
Installation consists of three parts: hardware, software and slot enabling.
Hardware installation consists of plugging the FPE into an expansion slot in the Apple II. This means that you
may use any slot numbered between 1 and 7. Don't try to use the memory expansion slot in the IIGS-it is not a
peripheral slot. The slot you choose will be dictated by the slots you have available.
Note that there are only two ways you can damage the board during installation - static electricity and putting
the board in backwards. If you carefully observe the following instructions, neither will be a problem:
1. Ensure all power to your computer is off by removing the power cord from the wall outlet.
2. Carefully remove the case cover from your computer as described in the owner's manual supplied by
3. Face the computer as you normally would if using it (keyboard toward you. Refer to Figure 2-1.).
4. Ground yourself by touching the top
of the metal cover of the power
supply on the left hand side of the
5. Remove the FPE from the box and the
anti-static plastic wrapping.
6 Plug the FPE into the slot of your
choice, ensuring that the component
side of the board (the side with the
lettering) faces to your right, away
from the power supply.
7. Replace the case cover, plug the
computer power cord into the power
outlet, apply power, and boot your
computer as normal.
FIGURE 2- L FPB En.ulUliofl 8. The computer should boot normaUy.
9. The computer is now ready for software installation.
Software installation requires booting the FPETOOLS distribution disk. The software on this this disk will
move certain files from the tS installation disk to your system disk.
1. Enable the slot if you have a IIGS and the slot requires enabling to use "YOUR CARD" (see Slot
Enabling). Then power down the computer.
2. Boot the FPETOOLS installation disk. The disk will automatically locate the FPE and report the slot
number to you.
3. Select option 3 from the Installation Menu. This test will verify that the FPE functions correctly.
Side of FPE
t , If the installation software reports an error or your system hangs, verify that you
have installed the FPE correctly (power down your system first, then reboot) and
verify that you have enabled the slot (set it to "Your Card"), if you have an Apple
IIGS. If the rerunning the test returns an error or your system hangs, please contact
Innovative Systems for technical support
2. If the test does not return (the system hangs) and you have an Applied Engineering
Trans Warp GS™, you will need to contact AE to obtain a modification to the
TWGS. Contact AE customer support for more information.
4. If you have a IIGS, select option 1 too install the FPE Toolset on your system disk(s). Note that if
your system disk is named "/hardl", for example, the disk name you should enter when requested is
"/hardl". No directory information is required. After successful installation, all SANE calls
(TOOL010 or SxxxA) will then automatically access the FPE without any need to recompile,
reconfigure, or replace any of your existing commercial or user- written software that uses the
5. If you have AppleWorks Classic, select option 2 to install a patch which provides the capability for
AppleWorks to use the FPE when doing math. Because AppleWorks can be in a subdirectory,
please provide the volume name and the subdirectory in response to the prompt from die
initialization program. For example, if AppleWorks is located in directory "/AppleWorks" on
volume "/hardl", please enter "/hard 1/Apple Works" when prompted. Also, if your Startup disk and
your Program disk are the same, enter (he same information after both prompts.
6. Select option to exit the installation program.
Innovative Systems has provided a FPE toolset initialization file, coded specifically for each slot. These slot
dependent files provide a small speed improvement over files which automatically locate the FPE slot, because
the code uses direct addressing of the FPE slots rather than using indirect indexed addressing. Thus, if the FPE
is in slot 2, you must have the file "FPETOOL.INIT.S2" in your "/SYSTEM/SYSTEM.SETUP" directory on
your startup disk.
NOTE: USE OF ANY FPETOOL.IN1T FILE NOT CORRESPONDING TO THE SLOT
NUMBER CONTAINING THE FPE WILL CRASH YOUR SYSTEM.
Optimized code for accessing the FPE from a higher level language will be included in the particular software
package you purchase (such as ORCA/C) and requires no installation on your part
The iS FPETOOLS installation disk also includes sets of macros (M8.FPE and M16.FPE), definitions (E8.FPE
and E16.FPE), and some examples for various development packages (APW, ORCA/M, MERLIN 8/16,
MERLIN 16+, LISA816) for those who wish to write their own code. Separate macro libraries are provided for
the 6502/65C02 and 65816 microprocessors. The user should use the macro library appropriate for his
computer. These files may reside anywhere on the user's disk. The macros are included in the folders
"FPE.IIGS" and "FPE.6502" on the installation disk.
2.3. Slot Enabling on the Apple IIGS
You may have to enable the slot in which the FPE is installed. Follow the instructions in your user's manual to
use the control panel to select "Your Card" for the appropriate slot. If you install the FPE in slot 3
(recommended), you do not need to enable the slot as it is always properly enabled.
2.4. Slot Enabling on the Apple II, 11+ , and //e
No enabling is required for Apple II, II+, or //e computers because the slot I/O is normally active.
3, Access to the FPE
How does the System know which slots contains the FPE?
1. If you have an Apple 1IGS and you have loaded the FPETOOL.INIT file corresponding to the slot
containing the FPE, all calls to SANE will automatically go to the FPE.
2. If you write your own code to directly access the FPE, you must use the correct address for the slot
locations: that is,
Sc080 + 16*slot_number (e.g., $c090 for slot 1).
Refer to Chapter 9 for information on how to determine the FPE slot number without hard coding
the slot number into your code.
Direct access means that software writes information directly to or reads data directly from the FPE
coprocessor interface registers. These interface registers reside in the 16 locations reserved for the slot in which
the card resides. These 16 locations are designated as Read-only, Write-only, or Read/Write, depending upon
their purpose. In using direct access, the software does not need to "pass through" unnecessary general purpose
Direct access is the most efficient method of communicating with the FPE. It eliminates overhead; this is not to
say it is always the best method of interfacing, however. Direct access programming requires a strong
understanding of programming. Chapters 5 and 6 contain additional information necessary to do direct
accessing of the FPE.
The Motorola MC68881 communicates with the host processor (6502, 65C02, or 65816) by way of Coprocessor
Interface Registers (CIR). These registers are used for control of, transferring operands to, and returning status
from the MC68881. The Apple II technical manuals and the Motorola "MC6888 1/68882 Floating-Point
Coprocessor User's Manual" contain valuable information on accessing the registers and details which explain
the uses for the CIRs. The iS FPE allows access to all the CIRs that are required to implement all MC68881
instructions. The only CIRs not accessible are those intended for use with the 68020/68030 microprocessors,
and which do not impact performance with the 6502/65816. The registers implemented in the FPE and their
base addresses are given in Table 3-1.
Table 3-1: Coprocessor Interface Register (CIR) Memory Map
1. All transfers are byte swapped from normal 6502/65816 storage; that is, the MSB of the data is
contained in the lowest memory address.
2. k is the number of the slot containing the FPE + 8.
3. Word transfers (16 bits) to the Operand register use addresses $C0kC and SCOkD. Multiple
word transfers (32, 64, 80, and 96 bits) use all four locations ($C0kC-$C0kF). Note that for
80-bit transfers, the first data transfer requires that $C0kE and SCOkF receive $0 values and
that bits 65 to 80 are transferred to $C0kC and SCOkD.
4. All locations are located in the I/O page ($00 or $E1) of 65816 RAM space.
5. All locations are in page SCO of the 6502 RAM space.
Remember that the register addresses are base addresses; so the address for a specific slot is specified by
replacing die k in the base address with 8 + slot number. For example, if the FPE is in slot 3, the Response
register starts at SCObO. Additional information on peripheral card addressing is available in Chapter 6,
"Programming for Peripheral Cards", pages 129-131 and 136-137 of the "Apple He Technical Reference
4. Interfacing to SANE
The Standard Apple Numerics Environment™ (SANE) defines a series of calls which provide numeric
operations in accordance with IEEE Standard 754 Binary Floating-Point Arithmetic. SANE also provides
several utility functions which include conversions of data from an ASCII representation to binary floating point
and back again. This environment provides very accurate numerics. Unfortunately, SANE operations can be
very slow. The iS FPE provides the numeric operations, but at a much faster rate.
Because SANE is standard with the Apple II computer, Innovative Systems provides numerics software
package which replaces most of the routines in the SANE toolset. The software uses the same calling
sequences, processes the commands in 80-bit precision, and generally provides the same results as those
described in the "Apple Numerics Manual", available from your Apple dealer. One difference is that the
transcendentals returned are slightly less accurate (76 bits or more of accuracy versus SO bits from SANE);
however, this change in accuracy should not adversely affect the performance of your software (see "Apple
Numerics Manual, Second Edition ", Chapters 28, and Chapter 10 of this manual for the details). Another
difference is that the FPE does not process COMP type variables; however, COMP calls will work with the FPE
toolset (except at the speed of the Apple II since the calls use the standard SANE code). Because the FPE
toolset is a hybrid of calls to the FPE and to the standard SANE toolset code, use of the FPE toolset is automatic
and transparent to most existing software.
4.1 Apple IIGS
To use the iS numerics software on an Apple IIGS, your must have copied the FPE.INTT from the iS source disk
to the /SYSTEM/SYSTEM. SETUP subdirectory on the system disk. This is normally done by the FPETOOLS
4.2 Apple II, II+, and//e
The replacement for the SANE interface in the Apple II.II+, or //e is customized (to a specific absolute memory
address) and is included on the FPETOOLS distribution disk in the "/FPETOOLS /FPE.6502/TOOLSET"
directory. This toolset uses the following calls:
jsr S2 100 to call the fp6502 routines
jsr $2104 to call the ELEMS6502 routines.
This toolset loads into locations beginning at 3(00)2100 and has a length of less than $1000 bytes. The toolset
has a filetype of BIN.
For more information, please refer to the "Apple Numerics Manual" available from Addison-Wesley Publishing
4.3 AppleWorks™ Classic
The replacement for the AppleWorks Classic calls to the 8-bit SANE software is included on the FPETOOLS
4.2 AppleWorks™ GS
Support for AppleWorks GS is automatically provided as this package uses the GS/OS and ProDOS 16 SANE
tool set calls.
5. How the FPE Transfers Data
The Innovative Systems FPE fully supports Motorola's MC68881 coprocessor dialog. The dialog consists of a
rigidly structured combination of commands and response primitives. The commands tell the MC6888 1 what to
do, and the primitives indicate actions that are required, including: transfer data, wait for synchronization, wait
for completion of operation, and handle error conditions. Failure to follow the coprocessor protocol can result
in destruction of your code during program execution.
The FPE allows three types of operations: Memory-to- Register (MEMREG), Register-to-Memory
(REGMEM), and Register-to-Register (REGREG). MEMREG and REGMEM operations may be done at any
precision. REGREG operations are always done in extended precision.
5.1 MEMREG and REGMEM Operations
MEMREG and REGMEM operations move data from Apple memory to a MC68881 floating point, control, or
status register, and from a MC6888 1 floating point, control, or status register to Apple memory (refer to the
flow charts in Figures 5-1 and 5-2). These operations are often called move-in or move-out operations,
respectively. They require that the software
1. Write a command word (16 bits) to the Command register ($C0k8)
2. Check the word in the Response register (SCOkO) for a Null Come-Again (CA) (any value other than
3. Transfer the operand byte(s) to or from the Operand register (SCOkC)
4. Check the word in the Response register (SCOkO) for a Null Release (i.e., the most significant bit
(CA bit) is equal to 0)
The S8000 and S8900 signify that the values are written the way the MC68881 expects to write them; however,
the 6502/65816 must read and write all data in byte reversed order ($0089 in this case). The reason for the byte
reversal is that the 6502 and the 65816 write the low byte of the accumulator to the low byte of memory or to a
peripheral slot. This is opposite to the requirements of the MC68xxx series. Hence, the 68881 expects or
reports the most significant byte (MSB) as the low address byte. You must transpose the byte order of all data
(including 80 bit data) to satisfy the MC68881. Remember this because it applies to every command or operand
transfer to, and operand and response transfer from, the FPE.
NULL COME- AGAIN
NULL ( <> 18900)
NULL ( <> $8900)
<CA BIT - 1)
NO NULL COME- AGAIN
(CA BIT - I)
NO NULL COME-AGAIN
FIGURE 5-1. MOVE-IN SEQUENCE (MEMREG)
FIGURE 5-2. MOVE-OUT SEQUENCE (REG MEM)
You might even be wondering why we check for a value of $8900. The answer is adaption. If the MC6888 1
was being used with an MC68020 microprocessor, the value read from the Response register would indicate the
number of bytes to be transferred. In FPE applications, the MC6888 1 does the same, but the 6502/65816 cannot
easily make sense of this value. So to improve processing time, Innovative Systems noted that $8900 is the
only response primitive that requires the 6502/65816 to wait before transferring data. Any other value from the
Response register of the iS FPE implementation indicates that the 6502/65816 may transfer an operand.
Warning: don't try to test for a non-$8900 value as this will confuse the MC6888 1 and destroy any data in the
5.2 REGREG Operations
REGREG operations are used for operations that do not require operand data from memory to register transfers
(refer to Figure 5-3). Examples include adding two registers (both registers having a data value), taking the sine
of a value in a register, or even transferring a constant value from the ROM internal to the MC6888 1 to a
register. The sequence of operations is:
NO NULL RELEASE
(CA BIT - 1)
(CA BIT - 0)
FIGURE 5-3. REGISTER/REGISTER SEQUENCE (REGREG)
5.3 Checking Status
1. Write the command to the Command
2. Check the Response register for a Null
Since there are no external operands, a REGREG
operation does not require that the software test for a
Null Response in the Response register as the
MEMREG and REGMEM operations do. Once it has
written the command to the Command register (with
correct byte order), the software need only test the
for the Null Release.
NOTE: Don't try to test for a non-$8900
value as this will confuse the MC68881 and
destroy any data in the FPE.
Example code segments for checking the status from the FPE are as follows:
assumes the location containing
the base address of the FPE is
in the direct page
check for Null Come-Again
Ioop2 Ida [<mc68881],y check for Null Release
loopl ldy ^response
Ida (mc68881),y check for Null Come-Again
; (location containing
; the base address of the FPE is
; somewhere in memory,
; location designated by
loop2 ldy Response
Ida (mc68881),y check for Null Release
Ida (mc68881),y always must read upper byte
6. Construction of an MC6888 1/MC68882 Command
Each command written directly to the floating point coprocessor Command register requires 16 bits of
information. The format for the command (as seen by the MC6888 1) is:
12 1 11 1 10
s s s
where [R/M] Field - Specifies the source operand address mode.
- The operation is register to register.
1 - The operation is memory to register or register
[SSS] (Source Specifier Field) - Specifies the source
register or data format.
If R/M a 0, specifies the source floating point
data register, FPm.
If R/M = 1, specifies the source data format
000 L Long Word Integer (32-bits)
001 S Single Precision Real (32-bits)
010 X Extended Precision Real (96-bits) 1
011 P Packed Decimal Real (96-bits)2
100 W Word Integer (16-bits)
101 D Double Precision Real (64-bits)
110 B Byte Integer (8-bits)
[DDD] (Destination Register) - Specifies the destination
floating point register, FPn.
[CCCCC] (Execution Command) - Specifies the operation to
1. Only 80 bits contain valid data, but 96 bits must be transferred.
2. Only 84 bits contain valid data, but 96 bits must be transferred.
3. See "MC6888 1/MC68882 Floating-Point Coprocessor User's Manual", pages 3-1, 3-2, and
3-7 for format information)
4. All operations which input data to the FPE transfer information from the source (SSS or
memory) to the destination register (DDD). This means that the source value is moved (e.g.,
added) to the destination register.
5. All register-to- register operations move data from the source register to the destination
register (e.g., the source register is added to the contents of the destination register).
The files E16.FPE and E8.FPE contain definitions for the R/M and Source Specifier fields, the Destination
Register field, and the Execution Command field. To define a command to add an extended real number to
register 1 do the following:
1. Get the Memory -to-Register Extended Precision value from the definitions table (Table 6.1-1)
2. Get the value for Floating Point Register 1 from Table 6.1-2 (%001). Put this value into the
Destination register field (DDD, bits 7-9). The command word should now be $4880.
3. Put the value for the command (FADD in Table 6.1-3) into bits 0-4. From the definition file, FADD
equals S22. The command word should now be S48A2. Remember that the word is in reverse
order as seen from the Apple computer, so reverse the data bytes. The value for the command is,
Similarly, a register 1 (SSS value) to register 2 (DDD value) add would have a final command value of
"%00 1000 1000000 10 r or $2205 in Apple memory.
Page 1 1
1. To make this process easier, iS has supplied macro files which will generate the most used
commands for you,
2. The 16-bit binary values for commands are given in non-Apple memory order in the
examples associated with Tables 6.1-3 and 6.1-4.
Table 6.1-1 MC6888 1 Command Primitives
Register- to- Memory Movement
Single Precision $6400
Long Integer $6000
Word Integer $7000
Byte Integer $7800
Double Precision 57400
Extended Precision $6800
Packed BCD $6c00*
Single Precision $4400
Long Integer $4000
Word Integer $5000
Byte Integer $5800
Double Precision $5400
Extended" Precision $4800
Packed BCD $4cOO
Extended Precision (only) $0000
Constant in ROM-to-Register Movement (see Table 6.1-4)
Extended Precision (only) $5c00
Memory- to-Control, Status or Instruction Register
Long Integer (only) $0000
Control, Status or Instruction Register-to- Memory
Long Integer (only) $2000
* The retrieval of a packed BCD value form the FPE requires a formatting value (k-
factor). The k-factor format is as follows (encoded twos complement integer (3-bits
in locations 3-5)):
-64 to - indicates the of significant digits to the right of the decimal point
(FORTRAN F format)
+ 1 to +17 - indicates the number of significant digits in the mantissa
(FORTRAN E format)
+ 17to+63 - treated as +17
Table 6.1-2 Register Values
Floating Point Register %000
Floating Point Register 1 %001
Floating Point Register 2 %0 10
Floating Point Register 3 %011
Floating Point Register 4 %100
Floating Point Register 5 % 101
Floating Point Register 6 % 1 10
Floating Point Register 7 % 1 1 1
Control Register $9000
Status Register $8800
Instruction Address $8400
Table 6.1.-3 Operations Values
Log base 10
Single precision divide
Single precision multiply
Compare SSS with DDD
Simultaneous sine and cosine*
*FSINCOS requires three registers, one source and two destination, and is a register-
to-register operation only. The form for this command is:
%0OSSSDDDOO0Oddd + operation
where: ddd = destination 2 register (cosine value)
DDD = destination 1 register (sine value)
SSS = source register
Table 6.1-4 Constant in ROM-to-Register Values
uses form : %0 1 1 1 1 DDDOOvvvvv
where: DDD = destination
wvvv = ROM value.
7. Macro Usage
The iS FPE comes with macro library files. These files are compatible with the APW, ORCA/M, LISA816, and
MERLIN assemblers. M16.FPE, in conjunction with the E16.EQU file, (for LISA816 use only Ml 6.68881)
contains macros for use with the 65816 microprocessor in the Apple IIGS. M8.FPE contains the macros for the
6502-based Apple computers. These macros are assembler specific and are contained in folders labeled for the
The macros define the command for each operation desired. You just need to supply the operation wanted, the
address of the correctly formatted data, and the registers) to use. These macros will load or retrieve the results
of the operation. The general format of the macros is as follows:
MEMREGv OPE RATTON_CODE,DESTTN ATION_FP_REGISTER J) AT AAD DRE S S
where v = precision of operation (X, D, S, L, W)
REGMEMv OPERATION_CODE,SOURCE_FP_REGISTER,DATA_ ADDRESS
where v = precision of operation (X, D, S, L, W)
REGREG OPERATION_CODE,SOURCE_FP_REGISTER t DESTrNATION_FP_REGISTER
MEMREG PRECIS ION;OPERATION_CODE; DESTINATION FP_REG I S TER; D AT A ADDRESS
where PRECISION = X, D, S, L, W
REGMEM PRECIS ION;OPERATION_CODE;SOURCE_FP_REGISTER; DAT A_AD DRESS
where PRECISION = X, D, S, L, W
Register-to-Reg is ter:
The source code below is an example of macro usage and shows the form for code which uses the FPE.
SAMPLE TASK FOR ADDING TWO EXTENDED
* PRECISION NUMBERS, SHOWING THE USE
2/AINCLUDE/M 1 6 .UTILITY
DIRECT PAGE LOCATION OF FPE
$00 ZERO DIRECT PAGE DATA
LOCATION OF FPE+2 PUT FPE ADDRESS ON STACK
STORE FPE ADDRESS IN DIRECT
FMOVE,FPl t EXT_l PUT DATA INTO FPE REGISTER 1
FADD JT1 £XT 2 ADD SECOND VALUE TO REGISTER 1
FMOVE*FPl,ANS 1 RETRIEVE THE ANSWER IN EXTENDED
H'COBO 0000' ASSUME SLOT 3
EXT = 2
FLOATING POINT EXTENDED DATA AREA
DC H'0000 0000 0000 8000 3FFF VALUE=1.0
DC H'0000 0000 0000 8000 3FFF
RESULT SHOULD BE '0000 0000 0000 8000 4000' OR 2,0
8. About the MC68881 and SANE
The information in this chapter is excerpted from the "Apple Numerics Manual, Second Edition" chapters 27,
28, and 29. While all the information in the SANE manual may pertain to the operation of the MC68881 in the
Macintosh II, the data here pertains only to the operation of the FPE when called by the FPE toolset.
Functions the same on both MC68881 and FPE software and SANE
The MC6888 1 and the FPE toolset return identical results for the following operations:
• square root
• round-to-integral value
• conversions between floating point formats
• absolute value.
For transcendental operations, the FPE gets results slighdy less accurate than those returned by SANE; for some
operations, the FPE gets different results for cases involving zero, Infinities, and NaNs.
The FPE returns slightly less accurate results than those returned by SANE in the following cases:
• binary scale (FPE truncates scale factors to 14 bits)
• base-e logarithm
• base-2 logarithm
• base-e logarithm of 1 + x
• base-c exponential
• base-2 exponential
■ base-e exponential minus 1
■ sine, cosine, tangent, arctangent
• integer exponentiation
• general exponentiation
• base-2 logarithm of 1 + x
• base-2 exponentiation minus 1
■ compound interest
■ annuity factor.
The FPE returns results with the same accuracy but behaves differently for zero, denormalized numbers,
Infinities, and NANs:
• round-to-integer (when out-of-range the FPE preserves the sign)
• truncate- to-integer (when out-of-range the FPE preserves the sign)
• binary logarithm (same results except for and Infinity).
All remaining operations available from SANE can be assumed to be as accurate and operate in the same
manner for calls to the FPE toolset.
Accuracy of the MC68881's elementary functions
For the elementary functions, both the SANE and the FPE (MC6888 1) packages have errors in the least
significant bits of the fraction part of the extended format results, but the SANE package errors rarely exceed
the last bit, whereas the FPE errors can extend to as many as five bits. Hence, for individual elementary
functions, both packages retum results nearly identical when rounded to single or double precision. For
complicated expressions involving elementary functions, the FPE is likelier to return an error in double
precision results than the SANE packages are.
Controlling the environment
The FPE toolset converts the standard SANE environmental control calls to those needed by the MC6888 1.
Halts and Traps
The FPE toolset handles halts in the same way that the SANE package does.
Traps are not supported.
9. Programming Hints
1. If the FPE returns SOdld in the response register, then the attempted operation was invalid. The only way to
recover, short of powering off the system, is to call SANEReset from the toolbox or to use the following code:
sta FPE_restore (base register + 6)
Ida FPE .restore
Note that this is a 16 bit operation. If you are using a 65G2/65C02-based system, you must do two 8-bit writes
and two 8-bit reads.
2. When using the FPE Toolset from Pascal, C, or Basic, save intermediate results in the extended format. Use
of other formats forces the compiler to convert your data values to and from extended, operations which will
increase the execution time of your programs.
3. Whenever possible, store intermediate results in the FPE. Register-to-register operations can provide more
than 10 times the performance of memory-to-register operations.
4. The FPE contains four (4) ID bytes which conform to the Apple standard. These bytes and their locations
where x = the slot number.
Before reading the data in these locations, slotROM must be enabled by writing a value to $(00)c00b. Once
done, the slot ROM must be disabled by writing a value to $c00a. Note that all accesses to the values should be
done with the computer in 8-bit (short) index or accumulator mode.
10. FPE Data and Register Formats
MC68881/68882 SIGNED INTEGER DATA FORMATS
MC68881/68882 REAL DATA FORMATS
■ SIGN OF FRACTION
■SIGN OF FRACTION
IMPLICIT BINARY POINT
SIGN OF MANTISSA
MC6888"! Z68882 PACKED BCD FORMAT
■SIGN OF MANTISSA
SIGN OF EXPONENT
USED ONLY FOR
+/- INFINITY OR NANS
IMPLICIT DECIMAL POINT -
MANTn is the nth digit of the mantissa.
EXPn is the nth digit of the exponent EXP3 is only
generated during a move out operation if the
source operand exponent exceeds the magnitude
of a three digit exponent; otherwise it is a dont
care. Only EXP0-EXP2 are used for input.
XXX are don't care bits, which are zero and ignored
Non-Zero, note 1
Non-Zero, note I
Table A-l. Packed BCD 5tring Definitions.
1. A decimal string with the SE and Y bits set, an exponent of SFFF, and a non-zero 16-digh decimal
fraction is a NAN.
2, If a non-decimal digit (5A...SF) appears in the exponent of a zero, the number is converted to a true zero.
NON-DATA FLOATING POINT REGISTERS
FLOATING POINT CONTROL REGISTER
FPCR EXCEPTION ENABLE BYTE
WARNING: DO NOT SET ANY BITS IN THIS BYTE!
FPCR MODE CONTROL BYTE
00 TO NEAREST
01 TOWARD ZERO
10 TOWARD MINUS INFINITY
11 TOWARD PLUS INFINITY
NOT A NUMBER
CONDITION CODE VERSUS RESULT DATA TYPE
RESULT DATA TYPE
Innovative Systems Page 23
FLOATING POINT STATUS REGISTER
FPSR FLOATING POINT CONDITION BYTE
FPSR QUOTIENT BYTE
SIGN OF QUOTIENT
FPSR EXCEPTION STATUS BYTE
INEXACT DECIMAL INPUT
DIVIDE BY ZERO
SIGNALLING NOT A NUMBER
— BRANCH/SET ON UNORDERED
FPSR ACCRUED EXCEPTION BYTE
DIVIDE BY ZERO