Applesoft: Internals--Floating Point Math Package (1 of 3)



Applesoft's floating point package provides a 9 digit scientific package for

evaluating numeric equations.  It supports trigonometric functions with

arguments in radians, exponents and logarithms to base e.



ABBREVIATIONS



 msb:   most significant bit or byte

 lsb:   least significant bit or byte

 eol:   end of line token ($00)



 A:  the 6502 accumulator

 X:  the 6502 X register

 Y:  the 6502 Y register

 Z:  the zero flag of the 6502 status register

 C:  the carry flag of the 6502 status register



A,X is a 16 bit number where A has the msb and X the lsb.



(Y,A) is the number or string whose address is in Y and A, with the

      msb in Y and the lsb in A.



FAC:    the floating point accumulator

ARG:    the ARGument register



REAL NUMBER FORMAT



The real number format used throughout Applesoft is: the exponent is a single

byte signed number (EXP) in excess of $80 form (the signed value has $80

added to it); the mantissa is 4 bytes (HO,MOH,MO,LO); the binary point is

to the right of the most significant bit.  Since in binary floating point

notation the msb is always 1, the number's sign replaces the msb when the

number is stored in memory in packed form.  The sign, though, is kept in a

separate byte (SGN) when only bit 7 is significant.  If the exponent is zero,

the number is zero, although the mantissa isn't necessarily zero.



Examples:



       EXP  HO   MOH  MO   LO   SGN



           Packed format

-10      84   A0   00   00   00

 10      84   20   00   00   00



             FAC format

-10      84   A0   00   00   00    FF

 10      84   A0   00   00   00    00



Arithmetic routine calling conventions for single argument functions (e.g.,

SGN, ABS or INT):



On entry the argument is in the FAC.

On exit the result is in the FAC.



Arithmetic routine calling conventions for two argument functions (e.g., FADD

and FSUB):



On entry the first argument is in the ARG.

On entry the second argument is in the FAC.

On exit the result is in the FAC.



FLOATING POINT REGISTERS



NOTE:  The TEMP locations may be used for other things when not used by the

floating point math package.



       FAC   ARG  TEMP1 TEMP2 TEMP3  RND

EXP    9D    A5    93    98    8A    C9

HO     9E    A6    94    99    8B    CA

MOH    9F    A7    95    9A    8C    CB

MO     A0    A8    96    9B    8D    CC

LO     A1    A9    97    9C    8E    CD

SGN    A2    AA      (packed format)



FLOATING POINT CONSTANTS



The following addresses point to useful numbers; they're packed and suitable

for use by most of the arithimetic routines including CONUPK and MOVMF.



 RND             00C9

 -32768          E0FE

 1               E913

 SQR (1/2)       E92D

 SQR (2)         E932

 -1/2            E937

 LN (2)          E93C

 10              EA50

 1000000000      ED14

 1/2             EE64

 LOG (2) base e  EEDB

 pi/2            F063

 pi*2            F06B

 1/4             F070





Apple Tech Notes





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This information is from the Apple Technical Information Library.



ArticleID: TECHINFO-0000074



19960724 15:55:27.00

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