Enhanced BASIC internals By Lee Davison. |
Floating point numbers.
Floating point numbers are stored in memory in four bytes. The format of the numbers is as follows.
Exponent | S | Mantissa 1 | Mantissa 2 | Mantissa 3 |
ExponentBASIC program memory use.This is the power of two to which the mantissa is to be raised. This number is biased to +$80 i.e. 2^0 is represented by $80, 2^1 by $81 etc. Zero is a special case and is used to represent the value zero for the whole of the number.SSign bit. This bit (b7 of mantissa 1) is one if the number is negative.Mantissa 1/2/3This is the 24 bit mantissa of the number and is normalised to make the highest bit (b7 of mantissa 1) always one. So the absolute value of the mantissa varies between 0.5 and 0.9999999403954 . As we know that the highest bit is always one it is replaced by the sign bit in memory.Example.Values represented in this way range between + and - 1.70141173x10^38
$82,$49,$0F,$DB = +3.14159274 nearest floating equivalent to pi | || | | | |\--+---+- = 0.785398185 absolute value of mantissa | | | \--------- = + b7 of mantissa 1 is zero | \------------- = x 2^2 = 4 mantissa to be multiplied by 4
A BASIC program is stored in memory from Ram_base upwards. It's format is ..BASIC variables memory use.$00 Start of program marker byte.. then each BASIC program line which is stored as ..start of next line pointer low byte.. and finally ..
start of next line pointer high byte
line number low byte
line number high byte
code byte(s)
$00 End of line marker byte$00 End of program marker byte 1If there is no program in memory only the start and end marker bytes are present.
$00 End of program marker byte 2
After the program come the variables and function references, all six bytes long, which are stored as ..String placement in memory.1st character of variable or function name (+$80 if FN name).. then for each type ..
2nd character of variable or function name (+$80 if string)
Numeric String Function Exponent String length BASIC execute pointer low byte Sign (bit 7) + mantissa 1 String pointer low byte BASIC execute pointer high byte Mantissa 2 String pointer high byte Function variable name 1st character Mantissa 3 $00 Function variable name 2nd character After the variables come the arrays, which are stored as ..
1st character of variable name.. and then each element ..
2nd character of variable name (+$80 if string)
array size in bytes low byte (size includes this header)
array size in bytes high byte
number of dimensions
[dimension 3 size high byte] (lowest element is zero)
[dimension 3 size low byte]
[dimension 2 size high byte] (lowest element is zero)
[dimension 2 size low byte]
dimension 1 size high byte (lowest element is zero)
dimension 1 size low byte
Numeric String Exponent String length Sign (bit 7) + mantissa 1 String pointer low byte Mantissa 2 String pointer high byte Mantissa 3 $00 The elements of every array are stored in the order ..
index1 [0-n], index2 [0-n], index3 [0-n]i.e. element (1,2,3) in an array of (3,4,5) would be the ..1 + 1 + 2*(3+1) + 3*(3+1)*(4+1) = 70th element(As array dimensions range from 0 to n element n will always be the (n+1)th element in memory.)
Strings are generally stored from the top of available RAM, Ram_top, working down, however if the interpreter encounters a line such as ..String descriptors in BASIC.100 A$ = "This is a string".. then the high/low pointer in the A$ descriptor will point to the string in program memory and will not make a copy of the string in the string memory.
A string descriptor is a three byte table that describes a string, it is of the format ..Stack use in BASIC.base = string length
base+1 = string pointer low byte
base+2 = string pointer high byte
GOSUB and DO both push on the stack ..BASIC execute pointer high byteFOR pushes on the stack ..
BASIC execute pointer low byte
current line high byte
current line low byte
command token (TK_GOSUB or TK_DO)BASIC execute pointer low byte
BASIC execute pointer high byte
FOR line high byte
FOR line low byte
TO value mantissa3
TO value mantissa2
TO value mantissa1
TO value exponent
STEP sign
STEP value mantissa3
STEP value mantissa2
STEP value mantissa1
STEP value exponent
var pointer for FOR/NEXT high byte
var pointer for FOR/NEXT low byte
token for FOR (TK_FOR)
Last page update: 14th July, 2003. | e-mail me |