------------------------------------------------------------------------------
EXTINT LIBRARY DOCUMENTATION : Sam Thomas <s@ghost.sh>
------------------------------------------------------------------------------
Library Aims
------------
I started this project with the intent of having an extensible library
capable of handling large integers that would assemble and work correctly on
a number of Operating Systems (Windows and Linux).
NOTE: Needs FASM to assemble correctly see references [1]
------------------------------------------------------------------------------
Constants and Data Types
------------------------
There are a number of constants provided by the library, they are used to
represent the sizes of data types for both internal library functionality, and
also for the end user's use.
Below is the table of constants provided by the library:
+---------------------+----------------------+
| Constant definition | Size in double words |
|---------------------|----------------------|
| INT_TYPE_64_BITS | 2 |
| INT_TYPE_128_BITS | 4 |
| INT_TYPE_256_BITS | 8 |
| INT_TYPE_512_BITS | 16 |
| INT_TYPE_1024_BITS | 32 |
| INT_TYPE_2048_BITS | 64 |
| INT_TYPE_4096_BITS | 128 |
+---------------------+----------------------+
| Special constants | Value |
|---------------------|----------------------|
| INT_TYPE_MAX_BITS | INT_TYPE_4096_BITS |
+---------------------+----------------------+
The values in the table above form the enumerated type defined in the C header
'extint_t', this is used for representing the type of a passed parameter.
For assembly language and assemblers with similar data definition syntax the
following may be used to allocate space for variable of one of the types in
the above table:
Example:
extint_example dd INT_TYPE_4096 dup(0h)
In C allocation is more simple; and uses the following list of type
definitions:
+-----------------+----------------------+
| Type definition | Size in double words |
|-----------------|----------------------|
| ext_int64 | 2 |
| ext_int128 | 4 |
| ext_int256 | 8 |
| ext_int512 | 16 |
| ext_int1024 | 32 |
| ext_int2048 | 64 |
| ext_int4096 | 128 |
| ext_int_max | (default) 128 |
+-----------------+----------------------+
Data definition is universal for all modern C compilers, and is shown below,
allocating space for the same variable as in the assembly language example:
Example:
ext_int4096 extint_example;
Additionally, the contents of each double word in the C data type may be
reference, using the '.part[...]' member of the variable, where ... is the
index of the double word within the variable.
Example:
printf("0x%08X%08X", extint_example.part[1], extint_example.part[0]);
The above example will output the lowest quad-word of the variable.
The special constant definitions represent the largest possible type of
integer that the library can handle, this may be changed, so the library can
have a smaller memory footprint or to add additional (larger) types. This will
be explained in the section entitled 'Customising the library'.
------------------------------------------------------------------------------
Function reference
------------------
Assignment functions
--------------------
function: extassign - assign a value to an ext_int* variable
------------------------------------------------------------------------------
Prototype:
void extassign (
void *extint_dest,
enum extint_t extint_type,
unsigned long int extint_length,
unsigned long int ...
)
Explanation:
extint_dest: the address of the extint variable to assign a value to;
extint_type: the type (size) of value represented by extint_dest (see
above section for definition of enumerated type);
extint_length: the length of the integer passed as variable arguments
in double words;
... : the numerical data to be assigned to the destination variable,
this should be passed as follows: 0x01, 0x80000000, 0x01, 0x0;
this will represent the number: 0x1800000000000000100000000.
function: extassign_zero - assign the value zero to an ext_int* variable
------------------------------------------------------------------------------
Prototype:
void extassign_zero (
void *extint_dest,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the extint variable to assign the value 0
to;
extint_type: the type (size) of value represented by extint_dest (see
above section for definition of enumerated type).
function: extassign_neg_one - assigns the value minus one to an ext_int*
variable
------------------------------------------------------------------------------
Prototype:
void extassign_neg_one (
void *extint_dest,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to assign the value
-1 to;
extint_type: the type (size) of value represented by extint_dest (see
above section for definition of enumerated type).
------------------------------------------------------------------------------
Simple arithmetic functions
---------------------------
function: extadd - add two ext_int* variables together and stores the result
------------------------------------------------------------------------------
Prototype:
unsigned long int extadd (
void *extint_dest,
void *extint_src,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to store the result
and that of the first addition operand;
extint_src: the address of the ext_int* variable to use as the second
addition operand;
extint_type: the type (size) of value represented by extint_dest and
extint_src (note, that both operands must be the same
size).
return value: returns 1 if there is carry produced from the addition,
that is the resultant cannot be fully stored in the
destination operand.
function: extsub - subtract two ext_int* variables and store the result
------------------------------------------------------------------------------
Prototype:
unsigned long int extsub (
void *extint_dest,
void *extint_src,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to store the result
and the first subtration operand;
extint_src: the address of the ext_int* variable to use as the second
subtraction operand;
extint_type: the type (size) of value represented by extint_dest and
extint_src (note, that both operands must be the same
size).
return value: returns 1 if there is borrow produced from the
subtraction that is the resultant cannot be fully
stored in the destination operand.
function: extneg - change the sign of the ext_int* variable
------------------------------------------------------------------------------
Prototype:
void extneg (
void *extint_dest,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to use as the first
operand, and that to store the result in;
extint_type: the type (size) of value represented by extint_dest and
extint_src (note, that both operands must be the same
size).
function: extinc - increment the ext_int* variable by 1
------------------------------------------------------------------------------
Prototype:
void extinc (
void *extint_dest,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to increment, and
that to store the result in;
extint_type: the type (size) of value represented by extint_dest and
extint_src (note, that both operands must be the same
size).
function: extdec - decrement the ext_int* variable by 1
------------------------------------------------------------------------------
Prototype:
void extdec (
void *extint_dest,
void extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to decrement, and
that to store the result in;
extint_type: the type (size) of value represented by extint_dest and
extint_src (note, that both operands must be the same
size).
------------------------------------------------------------------------------
Complex arithmetic functions
----------------------------
function: extdiv - divide two ext_int* variables
------------------------------------------------------------------------------
Prototype:
void extdiv (
void *extint_quot,
void *extint_resi,
void *extint_src,
void *extint_divisor,
enum extint_t extint_type
)
Explanation:
extint_quot: the address of the ext_int* variable to store the
quotient of the division operation;
extint_resi: the address of the ext_int* variable to store the residue
of the division operation;
extint_src: the address of the ext_int* variable 'source' (first
operand) of division (the variable to divide);
extint_divisor: the address of the ext_int* variable 'divisor' (second
operand) of division (the variable to divide by);
extint_type: the type (size) of the value represented by the inputs
and outputs to the function (note, all operands must be
the same type).
function: extidiv - divide two ext_int* variables (treating values as signed)
------------------------------------------------------------------------------
Prototype:
void extidiv (
void *extint_quot,
void *extint_resi,
void *extint_src,
void *extint_divisor,
enum extint_t extint_type
)
Explanation:
extint_quot: the address of the ext_int* variable to store the
quotient of the division operation;
extint_resi: the address of the ext_int* variable to store the residue
of the division operation;
extint_src: the address of the ext_int* variable 'source' (first
operand) of division (the variable to divide);
extint_divisor: the address of the ext_int* variable 'divisor' (second
operand) of division (the variable to divide by);
extint_type: the type (size) of the value represented by the inputs
and outputs to the function (note, all operands must be
the same type).
function: extmul - multiply two ext_int* variables
------------------------------------------------------------------------------
Prototype:
void extmul (
void *extint_dest,
void *extint_src,
void *extint_multiplier,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to store the result
of the multiplication;
extint_src: the address of the ext_int* variable to use as the first*
operand of the multiplication;
extint_multiplier: the address of the ext_int* variable to use as the
second operand of the multiplication;
extint_type: the type (size) of the value represented by the inputs
and outputs to the function (note, all operands must be
the same type).
*IMPORTANT: For faster multiplication make sure that the second number is the
smaller number; or if possible to test less complex, that is it has less set
bits than the first operand. (The function extmuls automatically optimises
the process by first checking the order of inputs and changing them if needed
before calling the multiplication function; however this causes some overhead;
so if possible specify the operands in the opimised order.
function: extmul - multiply two ext_int* variables (treating values as signed)
------------------------------------------------------------------------------
Prototype:
void extimul (
void *extint_dest,
void *extint_src,
void *extint_multiplier,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to store the result
of the multiplication;
extint_src: the address of the ext_int* variable to use as the first*
operand of the multiplication;
extint_multiplier: the address of the ext_int* variable to use as the
second operand of the multiplication;
extint_type: the type (size) of the value represented by the inputs
and outputs to the function (note, all operands must be
the same type).
*IMPORTANT: For faster multiplication make sure that the second number is the
smaller number; or if possible to test less complex, that is it has less set
bits than the first operand. (The function extimuls automatically optimises
the process by first checking the order of inputs and changing them if needed
before calling the multiplication function; however this causes some overhead;
so if possible specify the operands in the opimised order.
------------------------------------------------------------------------------
Optimised complex arithmetic functions
--------------------------------------
function: extmuls - multiply two ext_int* variables
------------------------------------------------------------------------------
Prototype:
void extmuls (
void *extint_dest,
void *extint_src,
void *extint_multiplier,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to store the result
of the multiplication;
extint_src: the address of the ext_int* variable to use as the first*
operand of the multiplication;
extint_multiplier: the address of the ext_int* variable to use as the
second operand of the multiplication;
extint_type: the type (size) of the value represented by the inputs
and outputs to the function (note, all operands must be
the same type).
function: extmuls - multiply two ext_int* variables (treating values as signed
)
------------------------------------------------------------------------------
Prototype:
void extimuls (
void *extint_dest,
void *extint_src,
void *extint_multiplier,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to store the result
of the multiplication;
extint_src: the address of the ext_int* variable to use as the first*
operand of the multiplication;
extint_multiplier: the address of the ext_int* variable to use as the
second operand of the multiplication;
extint_type: the type (size) of the value represented by the inputs
and outputs to the function (note, all operands must be
the same type).
------------------------------------------------------------------------------
Bitwise manipulation - shift functions
--------------------------------------
function: extshl - shift a ext_int* variable left by an amount
------------------------------------------------------------------------------
Prototype:
void extshl (
void *extint_dest,
void *extint_src,
unsigned long int shift,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to store the result
of the left shift;
extint_src: the address of the ext_int* variable to use as the source
to shift left;
extint_shift: the amount of bits to shift left (32-bit value);
extint_type: the type (size) of the value represented by the inputs
and outputs to the function (note, all operands must be
the same type).
function: extshl_single - shift a ext_int* variable left by bit
------------------------------------------------------------------------------
Prototype:
void extshl_single (
void *extint_value,
enum extint_t extint_type
)
Explanation:
extint_value: the address of the ext_int* variable to shift left;
extint_type: the type (size) of the value specified in extint_value to
shift left by one place.
function: extshl - shift a ext_int* variable right by an amount
------------------------------------------------------------------------------
Prototype:
void extshr (
void *extint_dest,
void *extint_src,
unsigned long int shift,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to store the result
of the right shift;
extint_src: the address of the ext_int* variable to use as the source
to shift right;
extint_shift: the amount of bits to shift right (32-bit value);
extint_type: the type (size) of the value represented by the inputs
and outputs to the function (note, all operands must be
the same type).
function: extshl_single - shift a ext_int* variable right by bit
------------------------------------------------------------------------------
Prototype:
void extshl_single (
void *extint_value,
enum extint_t extint_type
)
Explanation:
extint_value: the address of the ext_int* variable to shift right;
extint_type: the type (size) of the value specified in extint_value to
shift right by one place.
------------------------------------------------------------------------------
Bitwise manipulation - rotate functions
---------------------------------------
function: extrol - rotate a ext_int* variable left by an amount
------------------------------------------------------------------------------
Prototype:
void extrol (
void *extint_dest,
void *extint_src,
unsigned long int extint_rotate,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to store the rotated
result;
extint_src: the address of the ext_int* variable to rotate left;
extint_rotate: the amount of bits to rotate left by (32-bit value);
extint_type: the type (size) of the value represented by the inputs
and outputs to the function (note, all operands must be
the same type).
function: extror - rotate a ext_int* variable right by an amount
------------------------------------------------------------------------------
Prototype:
void extror (
void *extint_dest,
void *extint_src,
unsigned long int extint_rotate,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to store the rotated
result;
extint_src: the address of the ext_int* variable to rotate right;
extint_rotate: the amount of bits to rotate right by (32-bit value);
extint_type: the type (size) of the value represented by the inputs
and outputs to the function (note, all operands must be
the same type).
------------------------------------------------------------------------------
Bitwise manipulation - boolean (and derived) functions
------------------------------------------------------
function: extand - perform a bitwise and upon two ext_int* variables
------------------------------------------------------------------------------
Prototype:
void extand (
void *extint_dest,
void *extint_src,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to use as the first
operand of the function, also used to store the result;
extint_src: the address of the ext_int* variable to use as the second
operand of the function;
extint_type: the type (size) of the value represented by the inputs
and outputs to the function (note, all operands must be
the same type).
function: extor - perform a bitwise or upon two ext_int* variables
------------------------------------------------------------------------------
Prototype:
void extor (
void *extint_dest,
void *extint_src,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to use as the first
operand of the function, also used to store the result;
extint_src: the address of the ext_int* variable to use as the second
operand of the function;
extint_type: the type (size) of the value represented by the inputs
and outputs to the function (note, all operands must be
the same type).
function: extxor - perform a bitwise xor upon two ext_int* variables
------------------------------------------------------------------------------
Prototype:
void extxor (
void *extint_dest,
void *extint_src,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to use as the first
operand of the function, also used to store the result;
extint_src: the address of the ext_int* variable to use as the second
operand of the function;
extint_type: the type (size) of the value represented by the inputs
and outputs to the function (note, all operands must be
the same type).
function: extnot - perform a bitwise not upon a ext_int* variable
------------------------------------------------------------------------------
Prototype:
void extnot (
void *extint_dest,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to perform the
function upon, also used to store the result;
extint_type: the type (size) of the value represented by the inputs
and outputs to the function (note, all operands must be
the same type).
------------------------------------------------------------------------------
Binary comparison functions
---------------------------
function: extcmp - compares two ext_int* variables
------------------------------------------------------------------------------
Prototype:
unsigned long int extcmp (
void *extint_dest,
void *extint_src,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to use as the first
operand (that is the variable to compare against);
extint_src: the address of the ext_int* variable to use as the second
operand;
extint_type: the type (size) of the value represented by the inputs
and outputs to the function (note, all operands must be
the same type).
return value: returns 1 if first operand is above;
returns 0 if first operand is equal to second operand;
returns -1 if first operand is below the second operand.
function: exticmp - compares two ext_int* variables (using signed values)s
------------------------------------------------------------------------------
Prototype:
unsigned long int exticmp (
void *extint_dest,
void *extint_src,
enum extint_t extint_type
)
Explanation:
extint_dest: the address of the ext_int* variable to use as the first
operand (that is the variable to compare against);
extint_src: the address of the ext_int* variable to use as the second
operand;
extint_type: the type (size) of the value represented by the inputs
and outputs to the function (note, all operands must be
the same type).
return value: returns 1 if first operand is greater;
returns 0 if first operand is equal to second operand;
returns -1 if first operand is less than the second
operand.
------------------------------------------------------------------------------
Customising the library
-----------------------
To customise the library a few tools are required, namely FASM which can be
downloaded from the authors website [1]. Aside from that you will need a text
editor.
The library can of course be extended in other ways than that will be shown
here, but if you are willing to make code changes, etc. you are expected to
already have the knowledge to do so (as it's not a library specific task).
The customisation that is shown here is how to add a new data type to the
library, there is no feasible limit to the amount of bits that can be used as
the upper limit of a data type but here are the recommendations/theoretical
limits:
-> upper limit: 2^32 - 1 (4,294,967,295) bits;
-> format: multiple of 32 (i.e. 32, 64, 128, etc.).
Changes to files:
constant.inc:
...
INT_TYPE_1024_BITS = 32
INT_TYPE_2048_BITS = 64
INT_TYPE_4096_BITS = 128
...
Adding a new type requires it be of the same format (INT_TYPE_[...]_BITS),
where [...] indicates the amount of bits; the value of this constant is the
amount of double-words (multiples of 32) the new type will cast.
Should this type be larger than the existing types then the limits section
will need to be updated too:
...
INT_TYPE_MAX_BITS = [...]
Where the [...] will be the constant definition of the new type, for instance
if a type holding 8192 bits is to be added then the limit will be set like as
follows:
...
INT_TYPE_MAX_BITS = INT_TYPE_8192_BITS
Following this example; the library will need to be reassembled, and the C
header file should be modified. The changes that are needed are as follows:
extint.h:
...
enum extint_t { INT_TYPE_64_BITS = 2, ..., [...] }
Where the [...] should be replaced by the constant definition from the
assembly include file. The final modifications should be to add a 'typedef'
for the new 'type', this should be in the format below:
typedef struct {
unsigned long int part[INT_TYPE_{...}_BITS];
} ext_int{...};
Where the {...} should be replaced by the amount of bits for the new 'type',
the limits section in the C header should also be updated as needed:
#define INT_TYPE_MAX_BITS INT_TYPE_{...}_BITS
#define ext_int_max ext_int{...}
Where the {...} should be replaced by the amount of bits in the largest data
type. No code modifications should be needed to allow the new type to be added
unless it doesn't fit the requirements listed as the beginning of this
section.
------------------------------------------------------------------------------
References
----------
[1]: FASM download page: http://flatassembler.net/download.php
xorpse/EXTINT-Library
Extended integer library for handling large integers in C and assembly language. (NOT THREAD SAFE)
Assembly