8080/8085 floating-point arithmetic library user`s manual
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1. indicates the number of positions the decimal point was moved to the right or left to produce the abbreviated form shown The numbers could have been written just as easily as 6373E 6 or 74E S The 32 bit binary floating point format recognized by FPAL consists of three fields Ce mme IA 1 bit 8 bits 23 bits The sign field contains a zero if the number is non negative and a one if the number is negative The exponent field corresponds to the E notation in the example above and indicates the number of bit positions the integer form of the number must be shifted to put it in the form 1 nnn Except in the case of floating point zero the value in the exponent field is offset by a bias of 2 1 or 127 i e the stored exponent is 27 1 larger than the true exponent 8080 8085 FPAL Introduction The fraction field contains the 23 bits to the right of the binary point An implicit one bit is assumed at the left of the binary point if the floating point number is nonzero Example Integer Floating Point 00000001 hexadecimal 0 011111110000 0000 S me ERA me sign exp fraction or in hexadecimal 3F800000 The following lists make additional comparisons between decimal binary integer and binary floating point representations To save space the internal binary representation is shown in hexadecimal form Decimal Binary Integer 0 00000000 hex 1 00000001 12. Bl B2 B3 and Cl represent addresses of floating point numbers FPR is the address of the Floating Point Register and IP is the address where the result is to be stored First we must reserve storage for the FPR and floating point operands used in the equation This is done with DS assembler directive FPR A1 B1 A2 B2 A3 B3 C1 IP DS DS DS DS DS DS DS DS DS bb bh HHL hhh a H CO Next we must declare the FPAL subroutines to be external using the EXTRN directive EXTRN FSET FLOAD FMUL FADD FDIV FSTOR The equation is then computed by the following sequence of loads and calls Remember that FSET must be called before all other subroutines LXI PUSH LXI CALL LXI LXI CALL LXI CALL LXI CALL LXI CALL LXI CALL LXI CALL CALL LXI CALL LXI CALL LXI CALL LXI CALL LXI CALL B FPR B B 0 FSET B FPR D A1 FLOAD D B1 FMUL D IP FSTOR D A2 FLOAD D B2 FMUL D IP FADD FSTOR D A3 FLOAD D B3 FMUL D IP FADD D C1 FDIV D IP FSTOR B C POINTS AT THE FPR DEFAULT ERROR HANDLER TO BE USED FPRIS INITIALIZED POINTERS TO FPR AND A1 ARE LOADED AT IS LOADED INTO THE FAC POINTER TO B1 IS LOADED A1 B1 IS FORMED IN THE FAC POINTER TO IP IS LOADED A1 B1 STORED IN LOCATION ADDRESSED BY IP A218 LOADED INTO THE FAC A2 B21S FORMED IN THE FAC A1 B1 A2 B21S FORMED IN THE FAC A1 B1 A2 B218 STORED IN IP A3 IS LOAD
3. D E register pair FCMPR and FZTST return their results to register A FIXSD stores a fixed point number into memory FQFB2D stores a decimal floating point number into memory the other subroutines leave their results in the FAC The procedures described in this chapter with the exception of FQFD2B and FQFB2D save all 8080 or 8085 registers except those registers receiving results from the arithmetic operation called The FPAL routines do not have their own stacks but use the stack of the calling program The FSET routine uses the STKLN assembler directive to allocate 40 bytes of stack for use by FPAL This should be sufficient unless your program causes the FPAL routines to require multiple copies of stack storage This could occur because of interrupt procedures which call FPAL or because of user error handler recur sion Your program must add 40 extra bytes to STKLN for each level of FPAL invocation If you create your own stack the number of stack bytes needed by FPAL is likewise 40 40n where n is the number of FPAL invocation levels Appendix C summarizes all FPAL procedures and the error conditions they can return Error handling is described in detail in Chapter 4 NOTE The FPR initialization subroutine FSET must be called before any of the arithmetic procedures can be used otherwise the results are undefined Arithmetic Procedures 8080 8085 FPAL 3 2 FADD Floating Point Addition This subroutine adds a flo
4. FFFFFFFF 255 000000FF 255 FFFFFFO1 2 15 x 10 7FFFFF80 note f 3 40 x 10 1 17 approximately NOTES Binary Floating Point 00000000 3F800000 BF800000 437F0000 C37F0000 4EFFFFFF 7F7FFFFF 00800000 40490FDB 7FFFFFFF FFFFFFFF hex note 2 note 3 n infinity infinity 1 Thisisthe largest integer that can be converted to single precision floating point retaining the exact value Integer values within the interval FF000000 01000000 have exact single precision floating point representations Integer values outside this interval may or may not be exact upon conversion this con version being implemented according to the round to even rule as described in Appendix B 2 Thisis the largest number in the single precision floating point format This is the smallest positive number in the single precision floating point format 1 3 CHAPTER 2 FLOATING POINT RECORD PROCEDURES If vou plan to use FPAL procedures you must allocate 18 contiguous bytes of memory for the Floating Point Record FPR The FPR format is described in detail in Appendix A In general it is divided into four fields e Status field 1 byte e Error Handler Address field 2 bytes This is the address of the error recovery subroutine e Error field 2 bytes e Floating Point Accumulator or FAC This consists of a fraction field 11 bytes and an exponent field 2 bytes The remainder of this
5. PROCEDURES FADD Floating Point Addition 3 2 FSUB Floating Point Subtraction 3 2 FMUL Floating Point Multiplication A ae FDIV Floating Point Division 3 3 FSQRT Floating Point Square Root 3 3 FQFD2B Decimal to Binary Conversion 3 4 FQFB2D Binary to Decimal Conversion 3 5 FIXSD Floating Point to Integer Conversion 3 6 FLTDS Integer to Floating Point Conversion 3 6 FCMPR Floating Point Number Comparison 3 7 FZTST Compare FAC to Zero 3 7 FNEG Change Sign of FAC 3 8 FCLR Clear FAC to Zero 3 8 FABS Absolute Value 3 8 CONTENTS PAGE Sample Programs i basen a bosses damien 3 8 8080 Assembly Language Example 3 8 PLEZNIESS0 Example rSv CLER sis eus 3 10 CHAPTER 4 ERROR HANDLING Error Handling Operation 4 1 FERHND Default Error Handler 4 1 Error During Arithmetic Operation 4 1 Error During FQFD2B Operation 4 2 Error During FQFB2D Operation 4 2 Error During FIXSD Operation 4 2 Error During FCMPR Operation 4 2 Error During FZTST FNEG or FABS Operation 4 2 Other Calls to FERHND 4 2 Sample User Error Handlers 4 3 Ass
6. a reserved 18 byte work area used to col lect status and error information and as an accumulator for intermediate results The procedures supporting the FPR perform FPR initialization change error recovery options check the contents of FPR fields and pass numbers between the FPR and memory The FPAL also includes a default error handler subroutine This subroutine is called when an invalid number is used in a floating point operation or if overflow underflow or division by zero are not handled by an arithmetic subroutine You may also write your own error handler so long as it conforms to the formats described in this manual The FPAL can be used by assembly language or PL M programs The FPAL pro cedures reside in an ISIS II library FPAL LIB in object code form They are self contained and can be used in component OEM board or Intellec Microcomputer Development System environments In general the following steps must be observed to use the floating point library An area of memory must be reserved for the Floating Point Record FPR 2 If your program uses interrupts or if you create your own stack the appropriate amount of stack space must be allocated for use by FPAL as described at the the beginning of Chapter 3 3 The names of the FPAL procedures you plan to use must be declared to be external using the EXTRN directive in the ISIS II 8080 8085 assembly language or the EXTERNAL attribute in PL M 80 4 FPAL
7. be linked and counted only once Support Routines 259 bytes 3 Calling FADD or FSUB causes both subroutines to be linked into your program These subroutines link in FCLR FLOAD and the support routines all of which have been previously counted In addition FNEG is linked so that the additional space requirement for FADD FSUB becomes FADD FSUB 463 FNEG 43 506 bytes 4 FDIV and FCMPR link in only the FPAL support routines FMUL and FLTDS link in only the support routines and FCLR both of which are already counted Thus only the absolute count for these procedures need be considered 5 FABS FERROR FIXSD FSTAT FSTOR and FZTST link in no other procedures and only their absolute sizes need be considered 6 FCLR FERHND FLOAD and FNEG are all linked by other subroutines and included in those subroutines total byte count They need not be counted again if referenced separately Example To compute I FIXSD A B you must allow space for FSET 393 FERHND FLOAD FMUL 404 FCLR Support Routines 259 FIXSD 178 1234 bytes Procedure Timing When computing execution speeds of FPAL procedures you must be even more wary of absolutes than when computing size requirements We could list the follow ing times for the basic arithmetic operations FADD 0 7 milliseconds FSUB 0 7 FMUL 1 5 FDIV 3 6 FCMPR 0 3 8080 8085 FPAL Summary of FPAL Procedures These figures are only approximations however and
8. 8080 8085 FLOATING POINT ARITHMETIC LIBRARY USER S MANUAL Manual Order Number 9800452 03 Copyright 1977 1978 1979 Intel Corporation LLL intel Corporation 3065 Bowers Avenue Santa Clara California 95051 il Additional copies of this manual or other Intel literature may be obtained from Literature Department Intel Corporation 3065 Bowers Avenue Santa Clara CA 95051 The information in this document is subject to change without notice Intel Corporation makes no warranty of any kind with regard to this material including but not limited to the implied warranties of merchantability and fitness for a particular purpose Intel Corporation assumes no responsibility for any errors that may appear in this document Intel Corporation makes no commitment to update nor to keep current the information contained in this document Intel Corporation assumes no responsibility for the use of any circuitry other than circuitry embodied in an Intel product No other circuit patent licenses are implied No part of this document may be copied or reproduced in any form or by any means without the prior written consent of Intel Corporation The following are trademarks of Intel Corporation and may be used only to describe Intel products i iSBC Multimodule ICE Library Manager PROMPT iCS MCS Promware Insite Megachassis RMX Intel Micromap UPI Intellec Multibus uScope and the combination of ICE iCS iSBC MCS or RMX and a numerical s
9. ADD PROCEDURE FA OA EXTERNAL DECLARE FA OA ADDRESS END FADD FDIV PROCEDURE FA OA EXTERNAL DECLARE FA OA ADDRESS END FDIV FMUL PROCEDURE FA OA EXTERNAL DECLARE FA OA ADDRESS END FMUL FLOAD PROCEDURE FA OA EXTERNAL DECLARE FA OA ADDRESS END FLOAD FSTOR PROCEDURE FA OA EXTERNAL DECLARE FA OA ADDRESS END FSTOR FSTAT PROCEDURE FA BYTE EXTERNAL DECLARE FA ADDRESS END FSTAT DECLARE BYTE ARRAYS 8080 8085 FPAL DECLARE FPR 18 BYTE A1 4 BYTE A2 4 BYTE A3 4 BYTE B1 4 BYTE B2 4 BYTE B3 4 BYTE C1 4 BYTE IP 4 BYTE STATUS BYTE IP COMPUTED BY FOLLOWING CALLS I FSET MUST BE CALLED FIRST CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL FSET FPR 0 0 USE FERHND FLOAD FPR A1 FMUL FPR B1 FSTOR FPR IP FLOAD FPR A2 FMUL FPR B2 FADD FPR IP FSTOR FPR IP FLOAD FPR A3 FMUL FPR B3 FADD FPR IP FDIV FPR C1 FSTOR FPR IP I RETURN STATUS FIELD STATUS FSTAT FPR Arithmetic Procedures CHAPTER 4 ERROR HANDLING Error Handling Operation When an error occurs during an FPAL operation the following steps are taken 1 The address of the FPR is pushed onto the 8080 or 8085 stack 2 A code is placed in the B C register pair indicating which procedure was executing when the error was detected 3 Theerror code bits in the FPR s Status field are set to indicate the ty
10. Arithmetic Procedures 8080 8085 FPAL 3 8 FNEG Change Sign of FAC This subroutine negates complements the sign bit of the FAC if the contents of the FAC are nonzero 1 bit is changed to 0 and vice versa If the number in the FAC is zero no action is taken FNEG assumes that registers B and C address the FPR Examples 8080 8085 assembly language LXI B FPR REGS B C POINT TO FPR LXI D NEGNUM REGS D E ADDRESS NUMBER WHOSE SIGN IS TO BE NEGATED CALL FLOAD LOAD NEGNUM CALL FNEG NEGATE SIGN OF NEGNUM PL M 80 CALL FLOAD FPR NEGATE NUMBER ADDR CALL FNEG FPR FCLR Clear FAC to Zero This subroutine clears the FAC by loading it with a floating point zero see Appen dix B FCLR assumes the B and C registers point to the FPR Examples 8080 8085 assembly language LXI B FPR REGS B C POINT TO FPR CALL FCLR THE FAC IS ZEROED PL M 80 CALL FCLR FPR FABS Absolute Value This subroutine sets the floating point number in the FAC to its absolute value that is the sign bit is set to zero FABS assumes the B and C registers address the FPR Examples 8080 8085 assembly language LXI B FPR REGS B C POINT TO FPR CALL FABS SIGN BIT SET TO ZERO PL M 80 CALL FABS FPR Sample Programs 8080 Assembly Language Example The following assembly language example computes the weighted inner product IP A1 B1 A2 B2 A3 B3 C1 8080 8085 FPAL Arithmetic Procedures Al A2 A3
11. ED INTO THE FAC A3 B31S FORMED IN THE FAC A1 B1 A2 B2 A3 B3IS FORMED IN THE FAC A1 Bt A2 B2 A3 B3 C1 IS FORMED IN THE FAC A1 B1 A2 B2 A3 B3 C1 IS STORED IN IP 3 9 Arithmetic Procedures 8080 8085 FPAL 3 10 This example assumes the default error handler FERHND is to be used At the end of the computation you can check to see whether any errors occurred by executing the following code sequence CALL FERROR THE CUMULATIVE ERROR INDICATORS ARE RETURNED IN H L MOV A L ANI 11111000B MASK OFF THE OPTION BITS JNZ HELP AT LEAST ONE ERROR OCCURRED PL M 80 Example The following PL M 80 example computes the same weighted inner product as the assembly language example IP A1 B1 A2 B2 A3 B3 C1 Al A2 A3 Bl B2 B3 and C1 represent addresses of floating point numbers FPR is the address of the Floating Point Register and IP is the address where the result is to be stored We must first declare the FPAL subroutines used to be external procedures and reserve the FPR memory area as an array Declaring the operators to be arrays too ensures that they will occupy contiguous locations in memory thus allowing use of the dot operator in calling the subroutines For the sake of illustration the FSTAT function is also included in this example DEFINE EXTERNAL PROCEDURES FSET PROCEDURE FA OP1 OP2 EXTERNAL DECLARE FA OP1 OP2 ADDRESS END FSET F
12. ITE 0 FABS ERROR 11 STATUS CALL WRITE 0 FSQRT ERROR 12 STATUS END END USERSERROR FCMPR ERROR 12 STATUS CHAPTER 5 INTERFACE TO FPAL The FPAL procedures reside in object module form in the library FPAL LIB onthe ISIS II system diskette You need only declare the names of the FPAL procedures you use to be external and call them when they are needed When you have com pleted program development you must link the necessary floating point procedures to your object module FPAL procedure names are declared to be external using the EXTRN directive in assembly language or the EXTERNAL attribute in PL M The simplest way to do this is to create a file containing external declarations for the FPAL procedures you will be using then incorporate this file into your source program using the IN CLUDE control in the 8080 8085 assembler or PL M 80 compiler For example you might imbed the INCLUDE control in your source code as follows INCLUDE F1 FPEXTN SRC since the FPAL procedures reside in an ISIS II library they can be linked quite easily by linking the entire library The linker then scans your program and links only those procedures you need those that satisfy external references Linking is done at the ISIS II command level following successful assembly compilation to produce a relocatable 8080 or 8085 object module The PL M 80 library PLM80 LIB must be linked Example LINK F1 MYPROG OBJ FPAL
13. LIB PLM80 LIB TO F1 MYPROG LNK You can also specify individually the FPAL procedures you want linked from FPAL LIB If you choose to let the linker satisfy external references you should be sure you do not have external declarations for procedures you don t use For exam ple you would not want to create an include file containing external declarations for all FPAL procedures unless you plan to specify individual modules at the time you link FPAL LIB or intend to use all of them If your set of program modules includes PL M 80 or 8080 8085 assembly language modules that call FPAL routines and also includes other modules written in FORTRAN 80 none of which should call FPAL routines you should link your program modules together after translating using the three step sequence given below rather than as illustrated in the example above This is necessary to avoid incorrect references to certain routines in the FORTRAN 80 run time libraries that have the same public names as routines in FPAL LIB l Link together your FORTRAN relocatable object program s and the support libraries they need including the FORTRAN 80 run time libraries required for your environment refer to the SIS II FORTRAN 80 Compiler Operator s Manual but omitting PLMSO LIB The LINK output from this step will include a list of unresolved external names of routines in PLM80 LIB and also the unresolved external names of any PL M or assembly language routines cal
14. Mgec FACpin Block Control Block B 0 Error User Handler Bit Error C Error Field Handler Initialization B 0 Error User Handler Bit Error C Error Field Handler FQFD2B FPR FACbin lt MEMdec FRESET ERROR B C ERR HAND ADDR D E FAC lt 0 ERROR lt B C ERR HAND ADDR lt D E Initialization FPR FPR FPR FPR FPR Error Handling STATUS 0 FAC V FAC REG A STATUS MEM FAC FAC FAC MEM FAC 0 Table C 2 lists the error codes set by the FPAL procedures As was described in Chapter 4 when an error occurs a code is placed in the B C register pair indicating which procedure was running when the error was detected error codes are set in the Summary of FPAL Procedures C 2 Status and Error fields of the FPR and the error handler is called The default error handler may perform additional operations depending on which procedure was executing In the case of an invalid number in the FAC the Status field error bits and the IE bit are preset by FLOAD rather than being set by an arithmetic procedure The call to FERHND comes from the arithmetic procedure however Table C 2 FPAL Error Handling Summary FPAL Procedure FABS FADD Error Type FERHND Action FAC invalid No operation FERHND returns x UUUUU101 UUUUUO 11 OE Overflow Set FAC to largest smallest no overflow positive negative Status UUUUUO00 UUUUU100 UE Underflow FAC set to 0 Status set to UUUUUD00 UUUUUI01 IE FAC inval
15. PR REGS B C POINT TO FPR CALL FSTAT STATUS FIELD LOADED INTO REG A CALL FERROR ERROR INFO TO REGS H L In PL M 80 the corresponding operations would be DECLARE STATFUN BYTE ERRFUN ADDRESS STATFUN FSTAT FPR ERRFUN FERROR FPR CHAPTER 3 ARITHMETIC PROCEDURES This chapter describes the FPAL procedures for performing floating point arithmetic These procedures are FADD A subroutine to add floating point numbers FSUB A subroutine to do floating point subtraction FMUL A subroutine to multiply floating point numbers FDIV A subroutine to do floating point division FSQRT Asubroutine to compute the square root of a floating point number FQFD2B A subroutine to convert a decimal floating point number to binary FQFB2D A subroutine to convert a binary floating point number to decimal FIXSD A subroutine to convert a floating point number to an integer FLTDS A subroutine to convert an integer to a floating point number FCMPR A byte function to compare floating point numbers FZTST A byte function to compare the FAC to zero FNEG A subroutine to negate change the sign of the FAC FCLR A subroutine to clear the FAC to zero FABS A subroutine to set the FAC to its absolute value All of these subroutines assume that the B C register pair contains the address of the FPR If a second operand stored in memory is needed to perform an operation the address of that operand s low order byte is supplied in the
16. al number ADDRESS is a 16 bit address pointing to the first byte of the decimal number to be converted D D are ASCII representations of decimal digits and n is the same as LENGTH The value of the number represented by this record is SIGN D D D 109 CALE Zero is represented by setting all digits to zero or by setting LENGTH to zero CONTROL BLOCK DECIMAL NUMBER ADDRESS LENGTH SCALE SIGN REGS D E POINTER Figure 3 1 Control Block Format 3 4 8080 8085 FPAL Arithmetic Procedures Examples 8080 8085 assembly language DSIGN DS DSCALE DS DLNGTH DS DADDR DS DEFINE CONTROL BLOCK N po PROGRAM MUST SCAN DECIMAL NUMBER AND LOAD NECESSARY INFORMATION INTO CONTROL BLOCK LXI B FPR REGS B C POINT TO FPR LXI D DSIGN REGS D E POINT TO CONTROL BLOCK CALL FQFD2B CONVERSION DONE RESULT STORED IN FAC PL M 80 DECLARE CONTROL STRUCTURE SIGN BYTE SCALE ADDRESS SLENGTH BYTE STRING PTR ADDRESS STRING m BYTE WHERE m IS GREATER THAN OR EQUAL TO CONTROL SLENGTH PROGRAM MUST SCAN DECIMAL NUMBER AND LOAD NECESSARY INFORMATION INTO CONTROL BLOCK CALL FQFD2B FPR CONTROL FQFB2D Binary to Decimal Conversion This subroutine converts a binary floating point number in the FAC to a decimal floating point number and stores the result in memory FQFB2D assumes that registers B and C contain the address of the FPR and that
17. am causes the FPAL routines to require multiple copies of stack storage This could occur because of interrupt procedures which call FPAL or because of user error handler recursion Your program must add 40 extra bytes to STKLN for each level of FPAL invoca tion If you create your own stack the number of bytes needed by FPAL is likewise 40 40n where n is the number of FPAL invocation levels Examples The following 8080 8085 assembly language sequence initializes the FPR and sets all bits in the Error field to zero The example also assumes you are using the default error handler LXI B FPR REGS B C POINT TO FPR PUSH B PUSH FPR ADDRESS ONTO STACK LXI B 0 USE DEFAULT ERROR HANDLER AND SET REG C ERROR FIELD TO ZEROS CALL FSET INITIALIZE FPR In PL M 80 the same operations can be done with the statement CALL FSET FPR 0 0 8080 8085 FPAL 8080 8085 FPAL Floating Point Record Procedures FRESET Reset Error Handling Procedure This subroutine is used to change the contents of the Error field or to specify that a different error handler be used A common use of FRESET is to reset the five error flags in bits 3 7 of the Error field s low order byte FRESET uses registers B and C in the same way as FSET figure 2 1 If bit 0 of register B is one registers D and E must contain the address of your error handler The shaded bits in figure 2 1 should always be set to zero The FAC and Status Fields are not affe
18. ating point number in memory to the number in the Floating Point Accumulator and leaves the sum in the FAC FADD assumes that registers B and C contain the address of the FPR and that registers D and E address the low order byte of the number in memory Examples 8080 8085 assembly language LXI B FPR REGS B C POINT TO FPR LXI D AUGEND REGS D E POINT TO AUGEND CALL FLOAD LOAD AUGEND INTO FAC LXI D ADDEND REGSD E POINT TO ADDEND CALL FADD ADD AUGEND AND ADDEND LXI D SUM REGS D E POINT TO SUM CALL FSTOR STORE RESULT IN SUM PL M 80 CALL FLOAD FPR AUGEND CALL FADD FPR ADDEND CALL FSTOR FPR SUM FSUB Floating Point Subtraction This subroutine subtracts a floating point number in memory from the number in the Floating Point Accumulator and leaves the result in the FAC FSUB assumes that registers B and C contain the address of the FPR and that registers D and E ad dress the low order byte of the number in memory Examples 8080 8085 assembly language LXI B FPR REGS B C POINT TO FPR LXI D MINEND REGS D E POINT TO MINUEND CALL FLOAD MINUEND LOADED INTO FAC LXI D SBHEND REGS D E POINT TO SUBTRAHEND CALL FSUB SUBTRACT SUBTRAHEND FROM MINUEND LXI D RESULT REGS D E POINT TO RESULT CALL FSTOR STORE RESULT PL M 80 CALL FLOAD FPR MINUEND CALL FSUB FPR SUBTRAHEND CALL FSTOR FPR RESULT FMUL Floating Point Multiplication This subroutine multiplies the numbe
19. chapter describes the procedures used to initialize and access FPR fields These procedures are FSET A subroutine to initialize the FPR FRESET A subroutine to reset the error handling procedures and flags FLOAD A subroutine to load a floating point number from memory into the Floating Point Accumulator FAC field of the FPR FSTOR A subroutine to store a floating point number from the FAC into memory FSTAT A byte function that places the Status field of the FPR into the 8080 or 8085 accumulator FERROR An address function that places the Error field of the FPR into 8080 or 8085 registers H and L The Floating Point Record may be initialized and modified only by the procedures described here The FSET initialization subroutine must be called before any other procedures are used otherwise the results are undefined The procedures described in this chapter save all 8080 or 8085 registers except those registers receiving results from the operation called FSET Initialize Floating Point Record This subroutine completes initialization of the FPR To initialize the FPR you must 1 Push the address of the FPR onto the 8080 or 8085 stack 2 Load register B with the error handler indicator load register C with the initial value for the Error Field 3 Load registers D and E with the address of a user defined error handler subroutine if necessary see below 4 Call FSET Before FSET is called registers B and C shou
20. cted by FRESET Examples The following 8080 8085 assembly language sequence clears the Error field mask bits to zero and specifies a user defined error handler whose symbolic address is ERRORI Registers B and C are initialized separately to show clearly the specifica tion of the error handler LXI B FPR REGS B C POINT TO FPR PUSH B PUSH FPR ADDRESS ONTO STACK MVI B 1 USE ERROR HANDLER ADDRESSED IN D E MVI C 0 CLEAR ERROR FIELD TO ZEROS LXI D ERROR1 POINTER TO ROUTINE ERROR1 CALL FRESET LOAD ERROR RECOVERY INFORMATION PL M 80 statements to perform the same operation would be DECLARE ERRORSFLAG LITERALLY 0000000100000000B CALL FRESET FPR ERROR FLAG ERROR1 FLOAD Load FAC from Memory This subroutine loads a floating point number from memory into the floating point accumulator FLOAD assumes that registers B and C contain the address of the FPR and that registers D and E address the low order byte of the 32 bit number in memory Examples The following 8080 8085 assembly language sequence loads a number whose sym bolic address is AUGEND into the FAC LXI B FPR REGS B C POINT TO FPR LXI D AUGEND REGS D E POINT TO AUGEND CALL FLOAD LOAD AND UNPACK AUGEND In PL M 80 the same number is loaded by CALL FLOAD FPR AUGEND FSTOR Store Number into Memory from FAC This subroutine stores the floating point number in the FAC into memory FSTOR assumes that registers B and C contai
21. d otherwise f 1 In both figures s is the sign bit 8080 8085 FPAL 8080 8085 FPAL Floating Point Record Format HIGH ADDRESS LOW ADDRESS POINTER Figure A 2 Floating Point Number Format in Memory Two FPAL subroutines operate on 32 bit integers FIXSD converts a floating point number in the FAC to an integer in memory FLTDS converts an integer in memory into a floating point number in the FAC The format of the 32 bit two s comple ment integer stored in memory is shown in figure A 3 In this figure 1 the high order bit is the sign bit HIGH ADDRESS LOW ADDRESS POINTER Figure A 3 Integer Format in Memory A 3 APPENDIX B DEFINITIONS This appendix defines terms used elsewhere in the manual along with the formulas used for rounding values and decoding exponent wraparound Floating Point Zero The word with all bits equal to zero is defined as the unique floating point zero No other form for floating point zero is provided by FPAL Invalid Numbers All bit patterns are valid except those described here The first set of invalids are those whose exponent field is set to all ones This set is used for infinities indefinites pointers etc Infinities are defined as INF S bit 0 all other bits 1 INF all bits 1 The indefinite form is IND S 2 0 exponent bits all 1 fraction bits 0 A second set of bit patterns is currently defined as invalid These are numbers wh
22. de interpretation 000 No error 001 Attempted division by zero 010 Domain error e g Y 1 011 Overflow 100 Underflow 101 Invalid number in FAC 110 Invalid number in memory 111 Currently undefined Error Handler Address Field The Error Handler Address field contains the address of the error handler subroutine This may be the FPAL s default error handler FERHND described in Chapter 4 or a routine of your own In either case the address is loaded into this field by either the initialization subroutine FSET or the reset subroutine FRESET Error Field The bits in the Error field are used to accumulate error statistics Only five bits of this field are used currently If any of the JE OE UE ZE or DE bits is set the error described below has oc curred at least once since the last time the respective bit was set to zero by the FSET or FRESET subroutine Bit Interpretation IE Invalid operand OE Overflow error UE Underflow error ZE Attempted division by zero DE Domain error The remaining three bits of the low address byte are currently unused Setting any of these bits to one causes undefined results Floating Point Accumulator The Fraction and Exponent fields shown in figure A 1 actually contain an unpacked version of the format assumed for 32 bit floating point numbers in memory figure A 2 The f normalization bit shown in figure A 1 is implied in the packed for mat f 0 if the Exponent field is zero an
23. der byte of a 4 byte storage location The resulting integer is stored in this location in two s complement format See Appendix A figure A 3 Examples 8080 8085 assembly language LXI B FPR REGS B C POINT TO FPR LXI D FLTNUM REGS D E POINT TO FLTNUM CALL FLOAD LOAD FLOATING POINT NUMBER LXI D FIXNUM ADDRESS FOR STORING RESULT CALL FIXSD DO CONVERSION AND STORE RESULT PL M 80 CALL FLOAD FPR FPSNUMBERSADDRESS CALL FIXSD FPR INTEGERSADDRESS FLTDS Integer to Floating Point Conversion This subroutine converts a fixed point number 32 bit signed integer in memory to a floating point number and loads the result into the Floating Point Accumulator Conversion is done using unbiased rounding see Appendix B FLTDS assumes that registers B and C point to the FPR and that registers D and E address the low order byte of a 32 bit two s complement integer Examples 8080 8085 assembly language LXI B FPR REGS B C POINT TO FPR LXI D FIXNUM REGS D E POINT TO INTEGER CALL FLTDS CONVERT INTEGER TO FLOATING POINT ANDLOAD INTO FAC PL M 80 CALL FLTDS FPR INTEGERSADDRESS 8080 8085 FPAL Arithmetic Procedures FCMPR Floating Point Number Comparison This function compares a number in the Floating Point Accumulator to a floating point number in memory The resulting Status field settings are returned to the accumulator register A FCMPR assumes the B and C registers point to the FPR and that r
24. e number if the correct result was positive or negative respectively The Status field is set to UUUUUOO00 e If division by zero was attempted the FAC is set to an invalid number representing an indefinite result The s bit is zero all exponent bits are one and all fraction bits are zero The Status field is set to UUUUUI101 e If an invalid operand was encountered no operation is performed and FERHND returns to the calling subroutine e If none of these conditions holds FERHND simply returns to the calling subroutine 4 1 Error Handling 4 2 Error During FQFD2B Operation The FQFD2B procedure does not check for valid ASCII representations in the input operand If invalid data is used no error conditions are reported but the result is undefined Overflow or underflow may occur during the conversion In this case the error 1s regarded as an arithmetic error and the error is handled as described in the preceding section Error During FQFB2D Operation As in the case of FQFD2B overflow or underflow errors may result from an arithmetic operation within the conversion procedure These errors are handled by the arithmetic procedure involved If the FAC contains an invalid quantity when FQFB2D is called this procedure stores an asterisk in the SIGN position of the decimal representation see figure 3 1 and in digit positions D through D One of the following codes is stored in the first digit p
25. egisters D and E address the low order byte of the number in memory If the comparison is successful one of the following bit patterns is set in the Status field and loaded into register A U means the bit is undefined and reserved for FPAL use 100U U000 FAC number in memory 010UU000 FAC number in memory 001UU000 FAC number in memory Examples 8080 8085 assembly language LXI B FPR REGS B C POINT TO FPR LXI D FACNUM REGS D E POINT TO FACNUM CALL FLOAD LOAD FACNUM INTO FAC LXI D MEMNUM REGS D E POINT TO MEMNUM CALL FCMPR NUMBERS COMPARED STATUS TO REG A PL M 80 CALL FLOAD FPR FAC NUMBER ADDR STAT FCMPR FPR MEMORY NUMBERSADDR FZTST Compare FAC to Zero This function compares the number in the Floating Point Accumulator to zero and returns the Status field to the accumulator register A FZTST assumes that registers Band C address the FPR If the comparison is successful one of the following bit patterns is set in the Status field and returned to register A U means the bit is undefined and reserved for FPAL use 100UU000 FAC 0 010UU000 FAC gt 0 001 UU000 FAC lt 0 Examples 8080 8085 assembly language LXI B FPR REGS B C POINT TO FPR LXI D TSTNUM REGS D E POINT TO TEST NUMBER CALL FLOAD LOAD TEST NUMBER INTO FAC CALL FZTST COMPARE NUMBER TO 0 STATUS TO REG A PL M 80 CALL FLOAD FPR TEST NUMBERS ADDR STAT FZTST FPR 3 7
26. embly Language Example 4 3 PL M 80 Example uti REC RES 4 4 CHAPTER 5 INTERFACE TO FPAL APPENDIX A FLOATING POINT RECORD FORMAT APPENDIX B DEFINITIONS APPENDIX C SUMMARY OF FPAL PROCEDURES ILLUSTRATIONS FIGURE TITLE PAGE 2 1 Registers B C Format for FSET 2 2 3 1 Control Block Format 3 4 A 1 Floating Point Record Format A 1 A 2 Floating Point Number Format in MEMO unseren A 3 A 3 Integer Format in Memory A 3 TABLES TABLE TITLE PAGE C 1 FPAL Procedure Operation C 1 C 2 FPAL Error Handling Summary C 2 C 3 FPAL Procedure Sizes C 3 CHAPTER 1 INTRODUCTION What is FPAL The Floating Point Arithmetic Library FPAL contains basic floating point subroutines and functions referred to generically as procedures The operations provided are addition subtraction multiplication division value comparison negation clearing to zero absolute value square root conversion between decimal and binary floating point number representations and conversion between floating point and 32 bit signed integer formats All operations are single precision positive number range approximates 1 2 x 10 to 3 4 x 10 The single precision format is described below and in Appendix B In addition to these operations a number of procedures are provided to deal with the Floating Point Record FPR This is
27. id No operation FERHND returns UUUUU110 IE Invalid no in No operation FERHND returns memory IE IE ZE e FCLR No error conditions FAC invalid Invalid no in memory 000UU101 000UU110 If operands identical Status set to 100UU101 otherwise Status is 000UU101 FCMPR FAC set to indefinite s 0 e 1 f 0 Status set to UUUUU101 IE set FDIV UUUUUO01 Attempted division by 0 Others Others Same as Same as FADD same same FADD as FADD as FADD FERROR No error conditions FIXSD FAC no too Set memory to largest smallest integer from FAC overflow positive negative Status UUUUUDO00 No operation FERHND returns No error UUUUU101 Not called Same as Same as Same as Same as FADD FADD FADD FADD FAC invalid Not called Decimal record sign and D D set to D set to if FAC INF if FAC INF 2 if FAC IND 0 if FAC 0 all other invalids UUUUU101 No error conditions large FAC invalid integer stored is undefined Number loaded into FAC is invalid FLOAD FLTDS FMUL UUUUUO 1 OE UUUUU 101 IE FNEG IE FQFB2D IE FQFD2B 8080 8085 FPAL 8080 8085 FPAL Summary of FPAL Procedures Table C 2 FPAL Error Handling Summary Cont d Procedure Sizes None but if MA UO or OO bits 1 results are undefined FAC invalid No ope
28. l oN i il IFA 1 2 3 4 AND IF THE ERROR CONDITION IS UNDERFLOW SET THE RESULT TO ZERO OTHERWISE SIMPLY RETURN FZTST FNEG FABS FSQRT CPI 9 JNC DONE CALL FSTAT ANI 00000111B CPI 4 JNZ DONE CALL FCLR RESTORE REGISTERS AND STACK DONE POP H POP B POP PSW INX SP INX SP RET END PL M 80 Example The following code tells the FPAL that a user routine USERSERROR is to be called when an error is detected and loads the address of the error routine into the FPR If the calling procedure required two operands the second operand s address is passed as the third parameter of USERSERROR DECLARE ERROR FLAG LITERALLY 0000000100000000B CALL FSET FPR ERRORSFLAG USERSERROR 8080 8085 FPAL The remainder of this example is code needed to print a message indicating which procedure was running when the error occurred 4 4 WRITE END WRITE PROCEDURE AFT BUFFER COUNT STATUS EXTERNAL DECLARE AFT BUFFER COUNT STATUS ADDRESS USERSERROR PROCEDURE FPR ERROR ADDR DECLARE FPR ERROR ADDR STATUS ADDRESS DO CASE ERROR CALL WRITE 0 FADD ERROR 11 STATUS CALL WRITE 0 FSUB ERROR 11 STATUS CALL WRITE 0 FMUL ERROR 11 STATUS CALL WRITE 0 FDIV ERROR 11 STATUS CALL WRITE 0 FIXSD ERROR 12 STATUS CALL WRITE 0 CALL WRITE 0 FZTST ERROR 12 STATUS CALL WRITE 0 F NEG ERROR 11 STATUS CALL WR
29. ld contain initial values as shown in figure 2 1 The shaded bits shown in this figure are reserved for FPAL use and should always be set to zero Ones in these bit fields currently cause undefined results Floating Point Record Procedures SESS NS Xt QU d A bee 0 4449 x EX uu eet A y N que mN tu bi AAA A du WAY ie Y ioco s Figure 2 1 Registers B C Format for FSET The EH bit register B is interpreted as follows EH 0 The default error handler FERHND is to be used EH 1 Your own error handler is to be used and its address must be found in registers D and E If EH 0 registers D and E are ignored If EH 1 FSET loads the contents of registers D and E into the Error Handler Address field of the FPR NOTE FSET always links an error handler named FERHND whether you specify your own error handling subroutine or not If your own subroutine has the same name as the default subroutine your error handler must appear before FPAL in the link list to ensure that your FERHND is linked instead of FPAL s LINK MYPROG OBJ FERHND OBJ FPAL LIB FSET also clears the FAC and Status fields to zero and loads the contents of register C into the low order byte of the Error field See Appendix A for a detailed explana tion of the register C bits In addition FSET uses the STKLN assembler directive to allocate 40 bytes of stack for use by FPAL This should be sufficient unless your progr
30. led from your FORTRAN program s These can be ignored 2 Link together your PL M 80 or 8080 8085 assembly language relocatable object program s and the support libraries they need but again omitting PLMSO LIB The LINK output will again include a list of unresolved external names of routines in PLM80 LIB and also the unresolved external names of any FORTRAN routines called from your PL M or assembly language pro gram s These again can be ignored 5 Interface to FPAL 8080 8085 FPAL 5 2 3 Link all modules together in this order if your main program is in FORTRAN LINK output from step 1 LINK output from step 2 PLM80 LIB Or link all modules in this order if your main program is in PL M or assembly language LINK output from step 2 LINK output from step 1 PLM80 LIB The LINK output from this step will include messages that certain symbols beginning with the letters FQ are multiply defined These messages can be ignored the pre linking steps 1 and 2 have ensured that the correct routines are linked to the calling modules that need them Example Your main program is written in FORTRAN 80 uses FORTRAN intrinsic functions so that FPEF LIB is needed and is stored in relocatable object form in FTNMN OBJ The main program calls two PL M 80 subroutines that call FPAL routines and also make ISIS II system calls so that SYSTEM LIB is needed The object code for these subroutines is in PLMSBI OBJ a
31. n the address of the FPR and that registers D and E contain the address of the low order byte of a 32 bit memory location 2 3 Floating Point Record Procedures 8080 8085 FPAL 2 4 Examples This 8080 8085 assembly language example stores the contents of the FAC into the memory location addressed by RESULT LXI B FPR REGS B C POINT TO FPR LXI D RESULT REGS D E POINT TO RESULT CALL FSTOR STORE FAC CONTENTS The store is done in PL M 80 by CALL FSTOR FPR RESULT FSTAT Access Status Information This function is called to access the contents of the FPR s Status field FSTAT assumes the address of the FPR has been loaded into the B and C registers When FSTAT is called the contents of the Status field one byte are returned in the accumulator register A Examples In 8080 8085 assembly language the Status field is loaded by LXI B FPR REGS B C POINT TO FPR CALL FSTAT STATUS FIELD LOADED IN REG A or in PL M 80 DECLARE STATFUN BYTE STATFUN FSTAT FPR FERROR Access Error Information This function is called to access the contents of the FPR s Error field It assumes the address of the FPR has been loaded into the B and C registers FERROR returns the Error field contents two bytes to registers H and L Examples This 8080 8085 assembly language example loads the contents of the Status and Er ror fields into the accumulator register A and into registers H and L respectively LXI B F
32. nd PLMSB2 OBJ You want to run your programs under ISIS II and use the software run time package for FORTRAN arithmetic If all the Intel libraries are on drive O and all your own program modules are on drive 1 you can use the following sequence of LINK commands 1 LINK F1 FTNMN OBJ F80RUN LIB F80ISS LIB amp FPEF LIB FPSOFT LIB TO F1 FTNMN LNK 2 LINK F1 PLMSB1 0BJ F1 PLMSB2 0BJ FPAL LIB amp SYSTEM LIB TO F1 PLMSB LNK 3 LINK F1 FTNMN LNK F1 PLMSB LNK PLM80 LIB 8 TO F1 MYPROG LNK APPENDIX A FLOATING POINT RECORD FORMAT The Floating Point Record is allocated as shown in figure A 1 EXPONENT FIELD FLOATING POINT ACCUMULATOR FRACTION FIELD 11 BYTES ERROR FIELD ERROR HANDLER ADDRESS FIELD LOW ADDRESS POINTER STATUS FIELD Figure A 1 Floating Point Record Format Status Field Six bits are currently defined in the Status field The setting of these bits depends on the floating point function performed The undefined bits are reserved for FPAL use The E G and L bits act as flags following a comparison FCMPR FZTST A number in the FAC is compared to a second number and ifthe FAC second operand if the FAC second operand if the FAC lt second operand rom Il pre u li Floating Point Record Format The three EC error condition bits indicate whether an error just occurred The type of error can be determined from these bit settings as follows Error Co
33. ose exponent field is zero with at least one other bit set to one Single Precision Format Single precision formats in the Floating Point Accumulator and 8080 or 8085 memory are as shown in figures A 1 and A 2 The three fields within these formats are s Sign bit Sign magnitude representation where s 0 means positive and s 1 means negative e Exponent bits Except in the case of floating point zero the exponent is offset by a bias of 2 1 i e the stored exponent is 2 1 larger than the true expo nent All zeros and all ones in the exponent field are currently reserved for the floating point zero and the invalid numbers described above f Fraction bits When the exponent is nonzero an implicit one bit is assumed at the left of the fraction the binary point is between the assumed bit and the ex plicit fraction bit The number base for the FPAL is binary The value of a given binary representation where s is the sign bit e is a binary exponent value and f is a binary fraction value can be formulated as s 2 1 1 1 f wheree 0ande FF B 1 Definitions B 2 8080 8085 FPAL Rounding If rounding is required to produce the final result of a floating point operation which do s not include FQFD2B and FQFB2D the round to even rule is used This rule returns the floating point number closest to the true result In the ambiguous case i e when two floating point number
34. osition D if the FAC contains INF wif the FAC contains INF af the FAC contains IND O if the FAC contains 0 if the FAC contains any other invalid quantity INF and IND are defined in Appendix B Error During FIXSD Operation If FERHND is called by FIXSD one of the following occurs e If overflow is indicated number in FAC too large to be converted to a 32 bit integer the result is set to the largest positive or negative integer if the number in the FAC is positive or negative respectively The FPR remains unchanged except that the Status field is set to UUUUUO00 e f the number in the FAC is invalid FERHND simply returns The integer stored by FIXSD is undefined Error During FCMPR Operation If FERHND is called by FCMPR at least one of the operands must be invalid If the operands are identical invalid bit patterns the Status field is set to 100UU101 Otherwise the Status field is OOOUU101 Error During FZTST FNEG or FABS Operation If the calling procedure is FZTST FNEG or FABS no operation is performed and the error handler simply returns Other Calls to FERHND If FERHND is called from somewhere other than the floating point procedures listed above the result is undefined 8080 8085 FPAL 8080 8085 FPAL Error Handling Sample User Error Handlers If you write your own handler and use FPAL arithmetic subroutines be aware that your error handler may be called rec
35. pe of error detected 4 The appropriate cumulative error bit in the FPR s Error field is set 5 Theerror handler subroutine is called The bit settings mentioned in steps 2 3 and 4 are listed in Appendix C Table C 2 If the executing procedure required a second operand that operand s address is in the D E register pair Otherwise the D E register pair is ignored FERHND Default Error Handler This subroutine is the error handler supplied as part of the floating point library You may also write your own error handler and load its address using the FSET or FRESET subroutines Chapter 2 The operations performed by FERHND depend on the parameters passed to it by the procedure detecting the error and on the error code found in the Status field These operations are described in the following paragraphs and summarized in Appendix C Table C 2 Note that FERHND may find it necessary to update the er ror code the three least significant bits in the Status field to reflect the current true status of the Floating Point Accumulator Error During Arithmetic Operation If FERHND was called during one of the four basic arithmetic operations FADD FSUB FMUL FDIV one of the following situations occurs e f underflow is indicated the FAC is set to zero and the Status field is set to UUUUU000 where U means the bit setting is undefined e If overflow is indicated the FAC is set to the largest or smallest representabl
36. procedure references must be imbedded in your source code where appropriate 5 TheFPAL procedure used by your program must be linked to your object file All FPAL procedures are reentrant and conform to PL M 80 linkage conventions If you plan to reference FPAL procedures in your program your program cannot use symbols that are reserved for FPAL To avoid using these symbols inadver tently do not use symbolic names beginning with a commercial at sign or names whose second character is Q or 1 1 Introduction 1 2 8080 8085 FPAL Single Precision Numbers FPAL procedures operate on single precision binary numbers either in a 32 bit integer format or in a 32 bit floating point format Integer Format The integer format recognized by FPAL is a positive or negative two s complement 32 bit binary number The approximate range of this format is Decimal Hexadecimal 42 147 x 10 7FFFFFFF 40 00000000 1 FFFFFFFF 2 147 x 10 80000000 Floating Point Format As an introduction to the single precision floating point format consider the following representations of very small and very large decimal numbers The decimal number base is used here to simplify the example Fixed Point Scientific Notation 6 373 000 000 6 373E 9 6 373 x 10 0 00074 7 4E 4 7 4 x 1077 The numbers in the two columns are equivalent In the second column the decimal point has been floated The exponent E
37. r in the Floating Point Accumulator by a floating point number in memory and leaves the product in the FAC FMUL assumes that registers B and C contain the address of the FPR and that registers D and E address the low order byte of the number in memory 8080 8085 FPAL Arithmetic Procedures Examples 8080 8085 assembly language LXI B FPR REGS B C POINT TO FPR LXI D MPCAND REGS D E POINT TO MULTIPLICAND CALL FLOAD MULTIPLICAND LOADED INTO FAC LXI D MPLIER REGS D E POINT TO MULTIPLIER CALL FMUL PERFORM MULTIPLICATION LXI D PRODUCT REGS D E POINT TO PRODUCT CALL FSTOR STORE PRODUCT PL M 80 CALL FLOAD FPR MULTIPLICAND CALL FMUL FPR MULTIPLIER CALL FSTOR FPR PRODUCT FDIV Floating Point Division This subroutine divides the number in the Floating Point Accumulator by a floating point number in memory and leaves the quotient in the FAC FDIV assumes that registers B and C contain the address of the FPR and that registers D and E address the low order byte of the number in memory Examples 8080 8085 assembly language LXI B FPR REGS B C POINT TO FPR LXI D DVDEND REGS D E POINT TO DIVIDEND CALL FLOAD DIVIDEND LOADED INTO FAC LXI D DIVSOR REGS D E POINT TO DIVISOR CALL FDIV PERFORM DIVISION LXI D QUOTNT REGS D E POINT TO QUOTNT CALL FSTOR STORE QUOTIENT PL M 80 CALL FLOAD FPR DIVIDEND CALL FDIV FPR DIVISOR CALL FSTOR FPR QUOTIENT FSQRT Floating Point Sq
38. ration FERHND returns Domain error FAC set to indefinite s 0 FAC e 1 f 0 Status set to negative UUUUU101 IE set No error conditions No error conditions FAC invalid No operation FERHND returns Table C 3 summarizes size information for each FPAL procedure in bytes These absolute figures must be read against the context of FPAL operation as a whole however as detailed in the notes following this table FPAL Procedure FABS FADD FSUB FCLR FCMPR FDIV FERHND FERROR FIXSD FLOAD FLTDS FMUL FNEG FQFB2D FQFD2B FRESET FSET FSQRT FSTAT FSTOR FZTST Support Routines Table C 3 FPAL Procedure Sizes Subroutines Linked FCLR FLOAD FNEG Support Routines None Support Routines Support Routines FCLR FLOAD None None None FCLR Support Routines FCLR Support Routines None ZEE FADD FABS FMUL FSTAT FDIV FIXSD FCMPR FZTST FMUL FNEG FDIV FLTDS FERHND FERHND NAM 35 56 C 3 Summary of FPAL Procedures 8080 8085 FPAL NOTES 1 FSET must be used Since it links in FERHND and FERHND links in FCLR and FLOAD the total space requirement for FSET is FSET 57 FERHND 227 FCLR 21 FLOAD 88 393 bytes Since FRESET links in the same subroutines as FSET they need not be counted again if FRESET is specified FRESET 40 bytes 2 A number of arithmetic procedures FADD FSUB FDIV FMUL FCMPR and FLTDS link in a set of FPAL support routines These routines need
39. registers D and E point to a control block in memory The control block has the format shown in figure 3 1 and points in turn to the memory location where the converted number is to be stored At the time FQFB2D is called you must also specify the contents of the LENGTH and ADDRESS fields of the control block The LENGTH field specification determines the precision of the result The first digit Dj is nonzero unless the FAC contains zero Example 8080 8085 assembly language DEFINE STORAGE AS IN THE FQFD2B EXAMPLE ABOVE DLNGTH SET 10 LENGTH FIELD SPECIFIED DADDR SET FOC8H ADDRESS FIELD SPECIFIED LXI B FPR REGS B C POINT TO FPR LXI D DSIGN REGS D E POINT TO CONTROL BLOCK CALL FQFB2D CONVERSION DONE RESULT STORED IN MEMORY 3 5 Arithmetic Procedures 8080 8085 FPAL 3 6 PL M 80 DECLARE CONTROL BLOCK STRUCTURE AS IN THE FQFD2B EXAMPLE ABOVE ASSIGN POINTER TO SOME STRING ARRAY CONTROL STRING PTR STRING ASSIGN VALUE FOR LENGTH OF STRING CONTROL SLENGTH 10 CALL FQFB2D FPR CONTROL FIXSD FloatingPoint to Integer Conversion This subroutine converts the floating point real number in the FAC to a fixed point integer number and stores the result in memory This conversion is done with truncation for example 1 9 is converted to 1 and 1 9 is converted to 1 FIXSD assumes that registers B and C contain the address of the FPR and that registers D and E address the low or
40. s are equally close to the true result the number with a zero in the least significant bit of the fraction is returned that 1s the nearest even number is returned Exponent Wraparound When overflow or underflow occurs during FPAL operations the correct fraction results but the exponent is wrapped around This is consistent with the FPAL development philosophy that no information should be lost and that you the user should be able to decide what you want to do when an overflow underflow excep tion occurs A wrapped around exponent is defined to be ey where the true offset exponent et can be derived from ey by considering an expanded range of exponents and on overflow 815 y 3 2 2 on underfiow ec ew 3 2 2 APPENDIX C SUMMARY OF FPAL PROCEDURES Basic Operation Table C 1 summarizes the input prerequisites of each FPAL procedure and the out put returned FERHND is not listed since it is called by other procedures not by the user Remember that FSET must be called before any other procedure Table C 1 FPAL Procedure Operation Procedure Addresses Addresses Stored at FABS FPR Ec FA FAC FAC FADD FAC FAC lt FAC MEM FCLR FAC FAC lt 0 FCMPR REG A FAC MEM FDIV FAC FAC lt FACIMEM FERROR REGS H L REGS H L ERROR FIXSD MEM MEMint FACip FLOAD FAC FAC lt MEM FLTDS FAC FACfp MEMint FMUL FAC FAC FAC MEM FNEG FAC 0 0 otherwise change sign ofFAC FQFB2D MEM Control ME
41. the actual figure for a given operation depends on the operands involved The following examples illustrate this point Example 1 Operand 1 40000000H Operand 2 40000000H Procedure FADD FSUB FMUL FDIV FCMPR Example 2 Operand 1 41C80000H Operand 2 41F00000H Procedure FADD FSUB FMUL FDIV FCMPR Example 3 Operand 1 41C8FF00H Operand 2 41FOFOFFH Procedure FADD FSUB FMUL FDIV FCMPR Example 4 Operand 1 3FFFFFFFH Operand 2 3FFFFFFEH Procedure FADD FSUB FMUL FDIV FCMPR ms 0 69 0 79 1 48 3 79 0 33 ms 0 70 0 83 1 43 3 60 0 28 0 66 0 83 1 54 3 60 0 28 ms 0 65 1 62 1 66 3 61 0 32 NOTE The only reason FSUB appears to take longer than FADD in these examples is that all operands are positive On the average both will take the same time since they are simply different entry points into the same subroutine C 5 8080 8085 Floating Point Arithmetic Library User s Manual 9800452 03 REQUEST FOR READER S COMMENTS The Microcomputer Division Technical Publications Department attempts to provide documents that meet the needs of all Intel product users This form lets you participate directly in the documentation process Please restrict your comments to the usability accuracy readability organization and completeness of this document 1 Please specify by page any errors you found in this manual 2 Does the document cover the informa
42. tion you expected or required Please make suggestions for improvement 3 Is this the right type of document for your needs Is it at the right level What other types of documents are needed 4 Did you have any difficulty understanding descriptions or wording Where 5 Pleaserate this document on a scale of 1 to 10 with 10 being the best rating NAME O DATE TITLE _ COMPANY NAME DEPARTMENT ADDRESS _ CITY STATE ZIPCODE Please check here if you require a written reply U WE D LIKE YOUR COMMENTS This document is one of a series describing Intel products Your comments on the back of this form will help us produce better manuals Each reply will be carefully reviewed by the responsible person All comments and suggestions become the property of Intel Corporation BUSINESS REPLY MAIL FIRST CLASS PERMIT NO 1040 SANTA CLARA CA POSTAGE WILL BE PAID BY ADDRESSEE Intel Corporation Attn Technical Publications M S 6 2000 3065 Bowers Avenue Santa Clara CA 95051 NO POSTA NECESSAF IF MAILEL IN U S A E I INTEL CORPORATION 3065 Bowers Avenue Santa Clara California 95051 408 987 8080 Printed in U S A
43. uare Root This subroutine takes the square root of the number in the Floating Point Accumulator and leaves the result in the FAC FSQRT assumes that registers B and C contain the address of the FPR Examples 8080 8085 assembly language LXI B FPR REGS B C POINT TO FPR LXI D ARG REGS D E POINT TO ARGUMENT CALL FLOAD ARGUMENT LOADED INTO FAC CALL FSQRT COMPUTE SQUARE ROOT LXI D RESULT REGS D E POINT TO RESULT CALL FSTOR STORE SQUARE ROOT RESULT 3 3 Arithmetic Procedures 8080 8085 FPAL PL M 80 CALL FLOAD FPR ARGUMENT CALL FSQRT FPR CALL FSTOR FPR RESULT FQFD2B Decimal to Binary Conversion This subroutine converts a decimal floating point number in memory to a binary floating point number and loads it into the FAC FQFD2B assumes that registers B and C contain the address of the FPR and that registers D and E point to a 6 byte control block in memory The control block in turn points to the decimal number to be converted Before calling FOFD2B you must define the control area and have the necessary information loaded into it The formats of the control block and decimal number are shown in figure 3 1 In this figure SIGN is the ASCII representation of or FOFD2B assumes a unless is specified SCALE is a 16 bit two s complement integer considered to be the exponent of ten LENGTH is an unsigned byte integer specifying the number of digits in the decim
44. uffix AR A BRL NB E ma e Printed in U S A A 168 280 15K CP This manual describes Intel s 8080 8085 Floating Point Arithmetic Library FPAL and its use FPAL extends the capabilities of programs written for the 8080 and 8085 microcomputers You can incorporate various floating point operations into your 8080 8085 assembly language or PL M 80 program using simple procedure calls The manual includes programming examples in both languages but assumes you already know how to use at least one of them Programming information can be found in the following manuals 8080 8085 Assembly Language 8080 8085 Assembly Language Programming Manual 9800301 ISIS II 8080 8085 Assembler Operator s Manual 9800292 PL M 80 PL M 80 Programming Manual 9800268 ISIS II PL M 80 Compiler Operator s Manual 9800300 PREFACE iii iv CHAPTER 1 PAGE INTRODUCTION WHatas PAL sid diam idees are eL 1 1 Single Precision Numbers 1 2 Integer FOLE us have ocak ane oe race ER uote dar ess 1 2 Floating Point Format 1 2 CHAPTER 2 FLOATING POINT RECORD PROCEDURES FSET Initialize Floating Point Record 2 1 FRESET Reset Error Handling Procedure 2 3 FLOAD Load FAC From Memory 2 3 FSTOR Store Number into Memory From FAC 2 3 FSTAT Access Status Information 2 4 FERROR Access Error Information 2 4 CHAPTER 3 ARITHMETIC
45. ursivelv and must therefore be reentrant Since FPAL does not have its own stack you must allocate 40 bytes of your own program stack for each level of recursion foreseen If you are writing your error handler in PL M it must be written and called with three parameters although the last parameter may actually be a dummy Assembly Language Example The following is an example of a reentrant error recovery routine ERREC If the calling program is FADD FSUB FMUL or FDIV and if the error condition is underflow the result is set to zero Otherwise the error recovery routine returns The address of the low order byte of the Floating Point Record is assumed to be on the stack and the B C register pair is assumed to contain the code indicating which procedure called ERREC If the procedure required two operands the second operand s address is assumed to be in the D E register pair NAME ERREC CSEG PUBLIC ERREC EXTRN FCLR FSTAT SAVE THE REGISTER CONTENTS PUSH PSW PUSH B PUSH H MOVE THE ERROR CODE TO A LOAD THE POINTER TO THE FPR INTO B C AND MOVE THE RETURN ADDRESS TO WHERE THE POINTER WAS 3 MOV A C PUSH D LXI H 8 DAD SP MOV E M INX H MOV D M INX H MOV C M INX H MOV B M MOV M D DCX H MOV M E POP D THE CODE SETTINGS IN A DESIGNATE WHICH PROCEDURE CALLED THE ERROR RECOVERY ROUTINE 1 FADD 2 FSUB 3 FMUL 4 FDIV 5 FIXSD 6 FCMPR 4 3 Error Handling gt Pp gt I
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