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FPU assembler programming By Erik H. Bakke Written 13/10-93 --- I ------------------------- INTRODUCTION ---------------------- I --- 1.1 Introduction Many people have asked me to explain how to program the 68881/68882/040 floating point coprocessors, and here it is, a guide in the "magic art" I have tried to keep this text as system neutral as possible, but it may, as the other articles in this series be influenced by the fact that I usually program at Amiga computers. If you need more information about the topics discussed herein, please contact the author. 1.2 Index Chapter I--------Introduction-------------------- 1.1 Introduction 1.2 Index Chapter II-----The Coprocessor interface--------- 2.1 The Interface mechanics 2.2 The Floating Point Coprocessor Chapter III----Floating Point Programming-------- 3.1 Floating Point Data Formats 3.2 Floating Point Constant ROM 3.3 Floating Point Instructions 1...Data transfer instructions 2...Dyadic operations 3...Monadic operations 4...Program control instructions 5...System control instructions Chapter IV-------The 68040 FPU------------------- 4.1 Differences 4.2 Instruction set Chapter V------------Sources--------------------- 5.1 Sourcecodes --- II -------------------THE COPROCESSOR INTERFACE -------------- II --- 2.1 The Interface Mechanics A coprocessor may be thought of as an extension to the main CPU, extending its register set and instructions. Different coprocessors that can be interfaced to the 68020+ CPU's are the 68881/2 FPU and 68851 MMU. Coprocessor instructions are placed inline with ordinary CPU codes, all recognized by being LINE-F instructions. (Having the op-code format of $Fxxx) In assembler, they are generally noted as cpXXXX instructions. The coprocessors require a communication protocol with the CPU for various reasons: ----------------------------------------------------------- 1. The CPU must recognize that a coprocessor is to receive the LINE-F op-code, and establish contact with that coprocessor. 2. The coprocessor may need to signal it's internal status to the CPU. 3. The coprocessor may need to read/write data to/from system memory or CPU registers. 4. The coprocessor may have to inform the CPU of error conditions, such as an illegal instruction or divide by zero. The CPU will have to process the corresponding exceptions. ----------------------------------------------------------- This protocol is called the MC68000 coprocessor interface. Knowledge of this interface is not required of a programmer who wishes to utilize a coprocessor, therefore I will not go into specific detail about the interface, but briefly sum up the main mechanisms. The coprocessor instructions are F-line instructions that have all bits in the upper nibble set to generate $Fxxx op-codes. Up to 8 coprocessors may reside on the bus (The Amiga coprocessors are NOT part of this system, and should not be counted in). Each of these co-processors have their own 3-bit address. Two such addresses are reserved by Motorola: %000 MC68851 PMMU %001 MC68881/2 FPU It is perfectly possible to install 6 FPU's in the same system. The general format of a coprocessor op-code is shown below: 15 1211 9 8 6 5 0 ================================ 1 1 1 1 Cp-ID Type Instruction dependent Followed by a number of coprocessor defined extension words and effective address extension words. If the instruction is not accepted by the coprocessor it is addressed to (if the CP is not present) the CPU will take an F-line exception. 2.2 The Floating Point Coprocessor The Motorola floating point coprocessor has the number 68881 or 68882. The 68882 is considerably faster than the 881, due to optimized internal design. In addition, the 68040 CPU has an internal FPU has is even faster than the 882. There are other differences between the 881/2 and the 040, but I'll return to those later. The 68881 and 68882 are pin compatible, and available in speeds up to 20Mhz and 50MHz respectively The FPU implements IEEE compatible floating point formats, and implements instructions to perform arithmetics on these formats, as well as several trancendental functions, such as SIN(x),E^x and so on. In addition the FPU has an on-chip constant ROM where different mathematical constants are stored. 2.2.1 The floating point registers The FPU has 8 floating point registers, each 80 bits wide. These are named FP0-FP7, just as D0-D7 in the CPU. In addition the FPU have 3 32-bit registers: Control Register FPCR 31.................15..........7..........0 Exeception Mode Enable Control Status Register FPSR 31.......23........15..........7..........0 Condition Quotient Accrued Exception Codes Exception Status Instruction Address Register FPIAR 31.......23........15..........7..........0 2.2.1.1 Floating point data registers The data registers always contain an 80 bit wide extended precision floating point number. Before any floating point data is used in calculation, it is converted to extended-precision. For example, the instruction FMOVE.L #10,FP3 converts the longword #10 to extended precision before transferring it to register FP3. All calculations with the FPU uses the internal registers as either source or destination, or both. 2.2.1.2 Floating Point Status Register This register is split in two bytes, the exception enable byte, and the mode control byte. 2.2.1.2.1 Exception Enable byte This register contains a bit for each of the possible eight exceptions that may be generated by the FPU. Setting or clearing one of these bits will enable/disable the corresponding exception. The exception bytes are organized this way: Bit Name Meaning ======================== 7 BSUN Branch/Set on UNordered 6 SNAN Signalling Not A Number 5 OPERR OPerand ERRor 4 OVFL OVerFLow 3 UNFL UNderFLow 2 DZ Divide by Zero 1 INEX2 INEXact operation 0 INEX1 INEXact decimal input 2.2.1.2.2 Mode control byte This register controls the rounding modes and rounding precisions. A result may be rounded or chopped to either double, single or extended precision. For most usage of the FPU, however, this register could be set to all zeroes, which will round the result to the nearest extended precision value. Mode control byte: Bit Name Meaning ======================== 7 PREC1 Precision bit 1 6 PREC0 Precision bit 0 5 RND1 Rounding bit 1 4 RND0 Rounding bit 0 3 ---- ----- 2 ---- ----- 1 ---- ----- 0 ---- ----- PREC=00 Round to extended precision PREC=01 Round to single precision PREC=10 Round to double precision RND=00 Round toward nearest possible number RND=01 Round toward zero RND=10 Round toward the smallest number RND=11 Round toward the highest number 2.2.1.3 Floating point Status Register This register is just what you may think it is, the parallell to the CPU CCR register, and reflects the status of the last floating point computation. The quotient byte is used with floating point remaindering operations. The exception status byte tells what exceptions that occured during the last operation. The accrued exception byte contains a bitmask of the exceptions that have occurred since the last time this field was cleared. Status bits: Bit Name Meaning ============================= 7 ---- ----- 6 ---- ----- 5 ---- ----- 4 ---- ----- 3 N Negative 2 Z Zero 1 I Infinity 0 NAN Not A Number 2.2.1.4 Floating point Instruction Address Register This register contains the address of the instruction currently executing. The FPU can execute instructions in parallell with the CPU, so that time-consuming instrcutions, such as division and multiplication don't tie up the CPU unnecessary. This means that if an exception occurs in the floating point operation, the address that are pushed on to the stack is not necessarily the address of the instruction that caused the exception. The exception handler would have to read this register to find the address of the offending instruction. --- III ----------------FLOATING POINT PROGRAMMING ------------- III --- 3.1 Floating Point Data Formats The FPU can handle 3 integer formats, and 2 IEEE compatible formats. In addition, it has an extended-precision format and can handle a Packed-Decimal Real format. 3.1.1 Integer Formats The 3 integer formats that are supported by the FPU are compatible with the formats used by the 68000 CPU's. They are Byte (8 bits), Word (16 bits), and Longword (32 bits). 3.1.2 Real Formats The FPU supports 4 real formats, the Single precision (32 bits), Double precision (64 bits), Extended precision (80 bits), and Packed-decimal string (80 bits) 3.1.2.1 Single Precision The single precision format is indicated with the extension .S It consists of a 23-bit fraction, an 8-bit exponent, and 1 bit indicating the sign of the fraction. The Single Precision format is defined by IEEE and uses excess-127 notation for the exponent. A hidden 1 is assumed as the most significant digit of the fraction. The format is defined as follows: 30 22 0 S EEEEEEEE FFFFFFFFFFFFFFFFFFFFFFF S=Sign of fraction E=Exponent F=Fraction The single precision format takes 4 bytes when written to memory. 3.1.2.2 Double Precision The double precision format is indicated with the extension .D It consists of a 52-bit fraction, an 11-bit exponent, and 1 bit indicating the sign of the fraction. As the single precision, this format is also defined by the IEEE, and uses excess-1023 notation for the exponent. A hidden 1 is assumed as the most significant digit of the fraction. The format is defined as follows: 62 51 0 S EEEEEEEEEEE FFFFFFF........FFFFFFFFFF S=Sign of fraction E=Exponent F=Fraction The double precision format takes 8 bytes when written to memory. 3.1.2.3 Extended precision The extended precision is indicated with the extension .X This is the format that is used in all computations, and consists of a 64-bit mantissa, a 15-bit exponent and 1 bit indicating the sign of the mantissa. A hidden 1 is not assumed, so all digits of the mantissa are present. Excess-16383 is used for the exponent. When data of this format is written to memory, it is "exploded" by 16 zero-bits between the mantissa and the exponent in order to make it longword aligned. The extended-precision format is defined as follows: 79 63 0 S EEEEEEEEEEEEEEE MMMMMMMMMMMMMMM............MMMMM When written to memory, it looks like this: 94 80 63 0 S EEEEEEEEEEEEEEE 000...000 MMMMMMMM...........MMM When written to memory, this format takes 12 bytes when written to memory 3.1.2.4 Packed-decimal string To simplify input/output of floating point numbers, a special 96-bit packed-decimal format. This format consists of 17 BCD digits mantissa, some padding bits, 4 BCD digits exponent, 2 control bits, 1 bit indicating the sign of the exponent, and 1 indicating the sign of the mantissa. Bits 68-79 are stored as zero bits unless an overflow occurs during the conversion. Positive and negative infinity is represented by numbers that are outside the range of the floating point representation used. If the result of an operation has no mathematical meaning, a NAN is produced. In the case of a NAN or infinity, bits 92 and 93 are both 1. 3.2 Floating point Constant ROM The FPU have an on-chip ROM where frequently used mathematical instructions are stored. How to retrieve these constants will be discussed below. Each constant has its own address in the ROM: Offset Constant ============================= $00 Pi $0b Log10(2) $0c e $0d Log2(e) $0e Log10(e) $0f 0.0 $30 ln(2) $31 ln(10) $32 10^0 $33 10^1 $34 10^2 $35 10^4 . . . $3e 10^2048 $3f 10^4096 3.3 Floating Point Instructions The FPU provides an extension to the normal 68000 instruction set. The floating point instructions can be divided into 5 groups: 1...Data transfer instructions 2...Dyadic instructions (two operands) 3...Monadic instructions (one operand) 4...Program control instructions 5...System control instructions The syntax and addressing modes for these instructions are the same as those of the ordinary 68000 instructions. 3.3.1 Data Transfer Instructions Instruction Syntax Op. Sizes Operation ================================================================== FMOVE FPm,FPn | X | The FMOVE instruction FMOVE <ea>,FPn | B/W/L/S/D/X/P | copies data from the FMOVE FPm,<ea> | B/W/L/S/D/X | source operand to the | | destination operand ================================================================== FMOVE FPm,<ea>(#k) | P | When writing a .P real, an FMOVE FPm,<ea>(Dn) | P | optional rounding precision | | may be specified as a constant | | or in a data register | | See below for details ================================================================== FMOVE <ea>,FPcr | L | These two FMOVE's copies FMOVE FPcr,<ea> | L | data to/from control registers ================================================================== FMOVECR #ccc,FPn | X | This instruction retrieves a | | constant from the ROM, where | | ccc is the offset to be read ================================================================== FMOVEM <ea>,<list> | L/X | Moves multiple FP registers FMOVEM <ea>,Dn | X | The register list may be FMOVEM <list>,<ea> | L/X | specified as in 68000 assembler, FMOVEM Dn,<ea> | X | or be contained as a bitmask | | in a data register ================================================================== When writing floating point numbers to the memory using the .P format, an optional precision may be specified as a constant or in a data register. Meaning of the precision: -64<=k<=0 Rounded to |k| decimal places 0<k<=17 Mantissa is rounded to k places Register bit mask of the MOVEM instruction: Addressing mode Bit 7 Bit 6 -------- Bit 1 Bit 0 ========================================================= -(An) | FP7 | FP6 |------| FP1 | FP0 | All other modes | FP0 | FP1 |------| FP6 | FP7 | ========================================================= 3.3.2 Dyadic Operations Dyadic operations are operations computing with two operands. The first operand may be addressed with any addressing mode, while the second operand (destination) must be an FPU register. Instruction Function =================================================== FADD | Add two FP numbers FCMP | Compare two FP numbers FDIV | FP Division FMOD | FP Modulo FMUL | Multiply two FP numbers FREM | Get IEEE remainder FSCALE | Scale exponent FSGLDIV | Single-precision Division FSGLMUL | Single-precision Multiplication FSUB | FP Subtraction =================================================== FSCALE adds the first operand to the exponent of the second operand. FREM returns the remainder of a division as specified by the IEEE definition. 3.3.3 Monadic Operations Monadic operations are operations computing with only one operand. The operand may be addressed with any addressing mode. The syntax of monadic operations are: Instruction.Size <ea>,FPn Instruction Function ==================================================== FABS | Absolute value FACOS | FP Arc Cosine FASIN | FP Arc Sine FATAN | FP Arc Tangent FATANH | FP Hyperbolic Arc Tangent FCOS | FP Cosine FCOSH | FP Hyperbolic Cosine FETOX | FP e^x FETOXM1 | FP e^(x-1) FGETEXP | Get exponent FGETMAN | Get mantissa FINT | FP Integer FINTRZ | Get integer and round down FLOGN | FP Ln(n) FLOGNP1 | FP Ln(n+1) FLOG10 | FP Log10(n) FLOG2 | FP Log2(n) FNEG | Negate a floating point number FSIN | FP Sine FSINH | FP Hyperbolic Sine FSQRT | FP Square Root FTAN | FP Tangent FTANH | FP Hyperbolic Tangent FTENTOX | FP 10^x FTWOTOX | FP 2^x ==================================================== There is one more monadic operation that uses a double destination operand, the FSINCOS instruction: FSINCOS <ea>,FPc:FPs Calculates sine and cosine FSINCOS FPm,FPc:FPs of the same argument All trigonometric operations operate on values in radians. 3.3.4 Program Control Instructions 3.3.4.1 Instructions This group of instructions allows control of program flow based on condition codes generated by the FPU. These instructions are parallells to the 68000 instructions with the same names. Instruction Formats Operation ===================================================================== FBcc <Label> | W/L | Branch on FPU conditions FDBcc Dn,<Label>| W | Test FPU conditions, decrement and branch FNOP | | No Operation (Like NOP) FScc <ea> | B | Set on FPU conditions FTST <ea> | All | Test FP number at <ea> FTST FPn | X | Test FP number in FPn ===================================================================== 3.3.4.2 Condition codes The FPU condition codes that may be acted upon are divided into two groups, with and without NAN exception. 3.3.4.2.1 Condition codes with NAN Symbol Meaning =========================================== GE | Greater or equal GL | Greater or less GLE | Greater, less or equal LE | Less or equal LT | Less NGE | Not (greater or equal) NGL | Not (greater or less) NGLE | Not (greater, less or equal) NGT | Not greater NLE | Not (less or equal) NLT | Not less SEQ | Signalling equal SNE | Signalling unequal SF | Signalling Always FALSE ST | Signalling Always TRUE =========================================== 3.3.4.2.2 Condition codes without NAN Symbol Meaning =========================================== OGE | Ordered and greater or equal OGL | Ordered and greater or less OR | Ordered OGT | Ordered and greater OLE | Ordered and less or equal OLT | Ordered less UGE | Unordered or greater or equal UEQ | Unordered or equal UN | Unordered UGT | Unordered or greater ULE | Unordered or less or equal ULT | Unordered or less EQ | Equal NE | Unequal F | Always FALSE T | Always TRUE 3.3.4.2.3 Notes You might wonder why there are different symbols for (unequal) and (greater or less). Floating point numbers may represent an infinity, something that is impossible in the 68000 CPU. In addition, they may represent illegal values (NAN). For detailed information on how these condition code symbols relate to the condition code flags, consult programming references for the 68881 FPU. 3.3.5 System Control Instructions This group consists of 3 instructions, FSAVE, FRESTORE and FTRAPcc. FSAVE and FRESTORE are priviliged instructions and are used to save and restore the FPU state frame to memory. FSAVE <ea> Copies the internal registers to the specified state frame FRESTORE <ea> Loads the internal registers with the specified state frame. The TRAPcc instruction can generate an exception dependant on the condition codes. FTRAPcc If the specified condition is true, TRAP. FTRAPcc #<data>.(W/L) --- IV --------------------------- THE 68040 FPU ----------------- IV --- 4.1 Differences The FPU that is built-in in the 040, and indeed in the yet to come 060 are highly optimized. It omits some instructions that are found on the 68881/2, but the ones that are unimplemented, are usually emulated in software. By avoiding the emulated instructions, a program can get a multiple speed increase when run on the 040. The 040 also omits the Packed Decimal format (.P) When it is attempted written, the 040 will respond with an illegal format exception. 4.2 Instruction set of the FPU-40 (Or whatever it is called) 4.2.1 68881/2 instructions that are unimplemented Type Instructions ================================================================= Monadic | FACOS,FASIN,FATAN,FATANH,FCOS,FCOSH,FETOX,FETOXM1, | FGETEXP,FGETMAN,FINT,FINTRZ,FLOG10,FLOG2,FLOGN, | FLOGNP1,FSIN,FSINCOS,FSINH,FTAN,FTANH,FTENTOX, | FTWOTOX Dyadic | FMOD,FREM,FSCAL,FSGLDIV,FSGLMUL Transfer | FMOVECR ================================================================= 4.2.2 68881/2 instructions that WORK on an 040 FABS ADD FBcc FCMP FDBcc FDIV FMOVE FMOVEM FMUL FNEG FNOP FRESTORE FSAVE FScc FSQRT FSUB FTRAPcc FTST --- V ----------------------------- SOURCES ----------------------- V --- 5.1 Sourcecodes There are no sourcecodes in this text, but in the same archive as you got this file there should be an assembler source for a julia fractal using the FPU. The program is a very simple one, and doesn't use the most advanced operations, but illustrates clearly how to program for the FPU. The program is written for Amiga computers with AGA chipset and at least OS 2.0, but it should be easy to degrade to earlier Amiga versions and to other platforms. ************************************************************************************************ * This text was written by Erik H. Bakke 14/10-93 © 1993 Bakke SoftDev * * * * This text is freely redistributable as long as all files are kept together and in unmodified * * form. * * Permission is granted to include this text in the HowToCode archive * ************************************************************************************************ * Error corrections, comments and questions should be directed to the author: * * * * e-mail: db36@hp825.bih.no * * phone: +47-5630-5537 (13:00-21:00 GMT) * * Post: Erik H. Bakke * * Bjørnen * * N-5227 SØRE NESET * * NORWAY * ************************************************************************************************