Variable-length quantity
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You are encouraged to solve this task according to the task description, using any language you may know.
Implement some operations on variable-length quantities, at least including conversions from a normal number in the language to the binary representation of the variable-length quantity for that number, and vice versa. Any variants are acceptable.
Task : With above operations,
- convert these two numbers 0x200000 (2097152 in decimal) and 0x1fffff (2097151 in decimal) into sequences of octets (an eight-bit byte);
- display these sequences of octets;
- convert these sequences of octets back to numbers, and check that they are equal to original numbers.
Ada
<lang Ada>with Ada.Containers.Vectors; with Ada.Text_IO; with Ada.Unchecked_Conversion;
procedure VLQ is
package Nat_IO is new Ada.Text_IO.Integer_IO (Natural);
type Byte is mod 2**8;
package Byte_IO is new Ada.Text_IO.Modular_IO (Byte);
type Int7 is mod 2**7;
package Int7_IO is new Ada.Text_IO.Modular_IO (Int7);
type VLQ_Octet is record
Value : Int7 := 0;
Next : Boolean := True;
end record;
pragma Pack (VLQ_Octet);
for VLQ_Octet'Size use 8;
function VLQ_To_Byte is new Ada.Unchecked_Conversion (VLQ_Octet, Byte); function Byte_To_VLQ is new Ada.Unchecked_Conversion (Byte, VLQ_Octet);
package VLQ_Vectors is new Ada.Containers.Vectors (Natural, VLQ_Octet);
procedure Hex_Print (Position : in VLQ_Vectors.Cursor) is
Value : Byte := VLQ_To_Byte (VLQ_Vectors.Element (Position));
begin
Ada.Text_IO.Put (':');
Byte_IO.Put (Item => Value, Width => 6, Base => 16);
end Hex_Print;
procedure Print (X : VLQ_Vectors.Vector) is
begin
X.Iterate (Hex_Print'Access);
Ada.Text_IO.New_Line;
end Print;
function To_VLQ (From : Natural) return VLQ_Vectors.Vector is
Result : VLQ_Vectors.Vector;
Current : Natural := From;
Element : VLQ_Octet;
begin
loop
Element.Value := Int7 (Current mod 2**7);
Result.Prepend (Element);
Current := Current / 2**7;
exit when Current = 0;
end loop;
Element := Result.Last_Element;
Element.Next := False;
VLQ_Vectors.Replace_Element (Result, Result.Last, Element);
return Result;
end To_VLQ;
function To_Int (From : VLQ_Vectors.Vector) return Natural is
use type VLQ_Vectors.Cursor;
Result : Natural := 0;
Iterator : VLQ_Vectors.Cursor := From.First;
begin
while Iterator /= VLQ_Vectors.No_Element loop
Result := Result * 2**7;
Result := Result + Natural(VLQ_Vectors.Element (Iterator).Value);
VLQ_Vectors.Next (Iterator);
end loop;
return Result;
end To_Int;
Test : VLQ_Vectors.Vector;
begin
Test := To_VLQ (16#7f#);
Nat_IO.Put (To_Int (Test), 10, 16); Ada.Text_IO.Put (" = ");
Print (Test);
Test := To_VLQ (16#4000#);
Nat_IO.Put (To_Int (Test), 10, 16); Ada.Text_IO.Put (" = ");
Print (Test);
Test := To_VLQ (16#0#);
Nat_IO.Put (To_Int (Test), 10, 16); Ada.Text_IO.Put (" = ");
Print (Test);
Test := To_VLQ (16#3FFFFE#);
Nat_IO.Put (To_Int (Test), 10, 16); Ada.Text_IO.Put (" = ");
Print (Test);
Test := To_VLQ (16#1FFFFF#);
Nat_IO.Put (To_Int (Test), 10, 16); Ada.Text_IO.Put (" = ");
Print (Test);
Test := To_VLQ (16#200000#);
Nat_IO.Put (To_Int (Test), 10, 16); Ada.Text_IO.Put (" = ");
Print (Test);
end VLQ;</lang>
Output:
16#7F# = :16#7F#
16#4000# = :16#81#:16#80#: 16#0#
16#0# = : 16#0#
16#3FFFFE# = :16#81#:16#FF#:16#FF#:16#7E#
16#1FFFFF# = :16#FF#:16#FF#:16#7F#
16#200000# = :16#81#:16#80#:16#80#: 16#0#
C
<lang c>#include <stdio.h>
- include <stdint.h>
int to_seq(uint64_t x, uint8_t *out) { int i, j; for (i = 7; i && !(x >> (8 * i)); i--); for (j = 0; j <= i; j++) out[j] = x >> (8 * (i - j));
return j; }
uint64_t from_seq(uint8_t *in, int len) { uint64_t r = 0; int i; for (i = 0; i < len; i++) r = (r << 8) | in[i];
return r; }
int main() { uint8_t s[8]; uint64_t x[] = { 0x7f, 0x4000, 0, 0x3ffffe, 0x1fffff, 0x200000, 0x3a1234df31413ULL};
int i, j, len; for (j = 0; j < sizeof(x)/8; j++) { printf("seq len %d: [ ", len = to_seq(x[j], s)); for (i = 0; i < len; i++) printf("%02x ", s[i]); printf("] back: %llx\n", from_seq(s, len)); }
return 0; }</lang>
D
This implements a Variable-length Quantity struct for an ulong integer.
<lang d>module vlq ; private import std.string ;
struct VLQ { // variable length quantity (unsiged long, max 63-bit)
ulong value ;
static ulong V2I(ubyte[] v) { return VLQ.init.from(v).value ; }
uint extract(ubyte[] v) {
ulong t = 0;
uint idx = 0, limit = v.length - 1 ;
if(8 < limit) limit = 8 ;
while ((idx < limit) && ((v[idx] & 0x80) > 0))
t = (t << 7) | (0x7f & v[idx++]) ;
if(idx > limit)
throw new Exception("too large for ulong or invalid format") ;
else
value = (t << 7) | v[idx] ;
return idx + 1 ;
}
VLQ from(ubyte[] v) { extract(v) ; return this ; }
@property
ubyte[] toVLQ() {
ubyte[] v = [(0x7f & value)] ;
ulong k = value >>> 7 ;
while(k > 0) {
v ~= (k & 0x7f) | 0x80 ;
k >>>= 7 ;
}
if(v.length > 9)
throw new Exception("value too large ") ;
return v.reverse ;
}
@property
string toStr() {
string s ;
foreach(e ; toVLQ)
s ~= std.string.format("%02X:", e) ;
return "("~s[0..$-1]~")" ;
}
static ulong[] split(ubyte[] b) {
ulong[] res ;
VLQ v ;
for(int i = 0, cnt = 1 ; i < b.length ; cnt++) {
auto k = v.extract(b[i..$]) ;
res ~= v.value ;
i += k ;
}
return res ;
}
alias value this ; // this allow VLQ works like ulong, eg add, multiply etc.
}</lang>
test code :
<lang d>import std.stdio ; import vlq ; void main() {
VLQ a = VLQ(0x7f), b = VLQ(0x4000), c ;
writefln("a:%8x = %s\nb:%8x = %s\nc:%8x = %s",
a.value, a.toStr, b.value, b.toStr, c.value, c.toStr) ;
c = (a + 1) * b ;
a = c - 1 ;
b = VLQ.init.from(a.toVLQ) ;
a <<= 1 ;
// convert ulong to octet sequence : VLQ(number).toVLQ
writefln("a:%8x = %s\nb:%8x = %s\nc:%8x = %s",
a.value, a.toStr, b.value, b.toStr, c.value, c.toStr) ;
//write them to a binary file
std.file.write("vlqtest.bin", a.toVLQ ~ b.toVLQ ~ c.toVLQ) ;
//read them back
auto buf = cast(ubyte[]) std.file.read("vlqtest.bin") ;
writefln("File length : %d", buf.length) ;
auto cnt = 0 ;
// convert octet sequence to ulong : (VLQ.init).from(octet sequence)
foreach(v; VLQ.split(buf))
writefln("%d:%8x = %s", 1 + cnt++, v, VLQ(v).toStr ) ;
}</lang>
output:
a: 7f = (7F) b: 4000 = (81:80:00) c: 0 = (00) a: 3ffffe = (81:FF:FF:7E) b: 1fffff = (FF:FF:7F) c: 200000 = (81:80:80:00) File length : 11 1: 3ffffe = (81:FF:FF:7E) 2: 1fffff = (FF:FF:7F) 3: 200000 = (81:80:80:00)
Groovy
Test examples borrowed from Java example
The Easy Way
Takes advantages of capabilities already built into the BigInteger type: <lang groovy>def testNumbers = [ 0x200000, 0x1fffff, 1, 127, 128, 589723405834L ]
testNumbers.each { BigInteger a ->
byte[] A = a.toByteArray()
A.each { printf "0x%02x ", it }; println ()
BigInteger a1 = new BigInteger(A)
assert a1 == a
}</lang>
Output:
0x20 0x00 0x00 0x1f 0xff 0xff 0x01 0x7f 0x80 0x89 0x4e 0x41 0x0e 0x0a
The Hard Way
Builds the byte arrays and numbers explicitly.
Solution: <lang groovy>final MASK = 2**8 - 1
def octetify = { n ->
def octets = []
for (def i = n; i != 0; i >>>= 8) {
octets << ((byte)(i & MASK))
}
octets.reverse()
}
def deoctetify = { octets ->
octets.inject(0) { long n, octet ->
(n << 8) + ((int)(octet) & MASK)
}
}</lang>
Test: <lang groovy>def testNumbers = [ 0x200000, 0x1fffff, 1, 127, 128, 589723405834L ]
testNumbers.each { a ->
def A = octetify(a)
A.each { printf "0x%02x ", it }; println ()
def a1 = deoctetify(A)
assert a1 == a
}</lang>
Output:
0x20 0x00 0x00 0x1f 0xff 0xff 0x01 0x7f 0x80 0x89 0x4e 0x41 0x0e 0x0a
Icon and Unicon
<lang Icon>procedure main() every i := 2097152 | 2097151 | 1 | 127 | 128 | 589723405834 | 165 | 256 do
write(image(i)," = ",string2hex(v := uint2vlq(i))," = ",vlq2uint(v))
end
procedure vlq2uint(s) #: decode a variable length quantity
if *s > 0 then {
i := 0
s ? while h := ord(move(1)) do {
if (pos(0) & h > 128) | (not pos(0) & h < 128) then fail
i := 128 * i + h % 128
}
return i
}
end
procedure uint2vlq(i,c) #: encode a whole number as a variable length quantity
if "integer" == type(-1 < i) then
return if i = 0 then
char((/c := 0)) | ""
else
uint2vlq(i/128,1) || char((i % 128) + ((/c := 0) | 128) )
end
procedure string2hex(s) #: convert a string to hex
h := ""
every i := ord(!s) do
h ||:= "0123456789abcdef"[i/16+1] || "0123456789abcdef"[i%16+1]
return h
end</lang>
Output:
2097152 = 81808000 = 2097152 2097151 = ffff7f = 2097151 1 = 01 = 1 127 = 7f = 127 128 = 8100 = 128 589723405834 = 9194f2849c0a = 589723405834 165 = 8125 = 165 256 = 8200 = 256
J
<lang j>N=: 128x v2i=: (N&| N&#./.~ [: +/\ _1 |. N&>)@i.~&a. i2v=: a. {~ [:;}.@(N+//.@,:N&#.inv)&.> ifv=: v2i :. i2v vfi=: i2v :. v2i</lang>
ifv is an invertible function which gets an (unsigned, arbitrary precision) integer sequence from a variable-length quantity sequence. vfi is an invertable function which gets a variable-length quantity sequence from an unsigned integer sequence. av displays character code numbers corresponding to the characters in its argument.
Example use:
<lang j> require'convert'
numbers=: 16b7f 16b4000 0 16b3ffffe 16b1fffff 200000 av vlq=: vfi numbers
127 129 128 0 0 129 255 255 126 255 255 127 140 154 64
av (vfi 1 2 3 4 5 6) +&.ifv vlq
129 0 129 128 2 3 130 128 128 2 129 128 128 4 140 154 70</lang>
Java
<lang java>public class VLQCode {
public static byte[] encode(long n)
{
int numRelevantBits = 64 - Long.numberOfLeadingZeros(n);
int numBytes = (numRelevantBits + 6) / 7;
if (numBytes == 0)
numBytes = 1;
byte[] output = new byte[numBytes];
for (int i = numBytes - 1; i >= 0; i--)
{
int curByte = (int)(n & 0x7F);
if (i != (numBytes - 1))
curByte |= 0x80;
output[i] = (byte)curByte;
n >>>= 7;
}
return output;
}
public static long decode(byte[] b)
{
long n = 0;
for (int i = 0; i < b.length; i++)
{
int curByte = b[i] & 0xFF;
n = (n << 7) | (curByte & 0x7F);
if ((curByte & 0x80) == 0)
break;
}
return n;
}
public static String byteArrayToString(byte[] b)
{
StringBuilder sb = new StringBuilder();
for (int i = 0; i < b.length; i++)
{
if (i > 0)
sb.append(", ");
String s = Integer.toHexString(b[i] & 0xFF);
if (s.length() < 2)
s = "0" + s;
sb.append(s);
}
return sb.toString();
}
public static void main(String[] args)
{
long[] testNumbers = { 2097152, 2097151, 1, 127, 128, 589723405834L };
for (long n : testNumbers)
{
byte[] encoded = encode(n);
long decoded = decode(encoded);
System.out.println("Original input=" + n + ", encoded = [" + byteArrayToString(encoded) + "], decoded=" + decoded + ", " + ((n == decoded) ? "OK" : "FAIL"));
}
}
} </lang>
Output:
Original input=2097152, encoded = [81, 80, 80, 00], decoded=2097152, OK Original input=2097151, encoded = [ff, ff, 7f], decoded=2097151, OK Original input=1, encoded = [01], decoded=1, OK Original input=127, encoded = [7f], decoded=127, OK Original input=128, encoded = [81, 00], decoded=128, OK Original input=589723405834, encoded = [91, 94, f2, 84, 9c, 0a], decoded=589723405834, OK
OCaml
<lang ocaml>let to_oct_seq n =
let rec aux n acc = let x = n land 0xFF and xs = n lsr 8 in if xs > 0 then aux xs (x::acc) else (x::acc) in aux n []
let to_num = List.fold_left (fun n x -> n lsl 8 lor x) 0
let v_rep n =
Printf.printf "%d\t" n; let seq = to_oct_seq n in List.iter (Printf.printf " 0x%02X") seq; print_char '\t'; let num = to_num seq in Printf.printf " %d\n%!" num; assert (n = num)
let () =
v_rep 0x200000; v_rep 0x1FFFFF;
- </lang>
Outputs:
$ ocaml variable_length.ml 2097152 0x20 0x00 0x00 2097152 2097151 0x1F 0xFF 0xFF 2097151
Perl
The vlg_encode sub returns an array of octets in most -> least significant order. Simply reverse the array to reverse the order.
<lang perl> use warnings; use strict;
for my $testcase (
0, 0xa, 123, 254, 255, 256, 257, 65534, 65535, 65536, 65537, 0x1fffff, 0x200000 )
{
my @vlq = vlq_encode($testcase); printf "%8s %12s %8s\n", $testcase, ( join ':', @vlq ), vlq_decode(@vlq);
}
sub vlq_encode {
my @vlq;
my $binary = sprintf "%s%b", 0 x 7, shift;
$binary =~ s/(.{7})$//;
@vlq = ( unpack 'H2', ( pack 'B8', '0' . $1 ) );
while ( 0 + $binary ) {
$binary =~ s/(.{7})$//;
unshift @vlq, ( unpack 'H2', pack 'B8', '1' . $1 );
}
return @vlq;
}
sub vlq_decode {
my $num; $num .= sprintf "%07b", hex(shift @_) & 0x7f while @_; return oct '0b' . $num;
} </lang>
Output:
0 00 0
10 0a 10
123 7b 123
254 81:7e 254
255 81:7f 255
256 82:00 256
257 82:01 257
65534 83:ff:7e 65534
65535 83:ff:7f 65535
65536 84:80:00 65536
65537 84:80:01 65537
2097151 ff:ff:7f 2097151
2097152 81:80:80:00 2097152
Perl 6
vlq_encode() returns a string of characters whose ordinals are the encoded octets. vlq_decode() takes a string and returns a decimal number. <lang perl6>sub vlq_encode ($number is copy) {
my $string = ;
my $t = 0x7F +& $number;
$number +>= 7;
$string = $t.chr ~ $string;
while ($number) {
$t = 0x7F +& $number;
$string = (0x80 +| $t).chr ~ $string;
$number +>= 7;
}
return $string;
}
sub vlq_decode ($string is copy) {
my $number = '0b';
for $string.ords -> $oct {
$number ~= ($oct +& 0x7F).fmt("%07b");
}
return :2($number);
}
- test encoding and decoding
for (
0, 0xa, 123, 254, 255, 256,
257, 65534, 65535, 65536, 65537, 0x1fffff,
0x200000
) -> $testcase {
my $encoded = vlq_encode($testcase);
printf "%8s %12s %8s\n", $testcase,
( join ':', $encoded.ords>>.fmt("%02X") ),
vlq_decode($encoded);
}</lang>
Output:
0 00 0
10 0A 10
123 7B 123
254 81:7E 254
255 81:7F 255
256 82:00 256
257 82:01 257
65534 83:FF:7E 65534
65535 83:FF:7F 65535
65536 84:80:00 65536
65537 84:80:01 65537
2097151 FF:FF:7F 2097151
2097152 81:80:80:00 2097152
PicoLisp
<lang PicoLisp>(de numToVlq (Num)
(let Res (cons (& Num 127))
(while (gt0 (setq Num (>> 7 Num)))
(push 'Res (| 128 (& Num 127))) )
Res ) )
(de vlqToNum (Vlq)
(let Res 0
(for N Vlq
(setq Res (| (>> -7 Res) (& N 127))) ) ) )
(for Num (0 15 16 127 128 255 2097151 2097152)
(let Vlq (numToVlq Num)
(tab (12 12 12) Num (glue ":" (mapcar hex Vlq)) (vlqToNum Vlq)) ) )</lang>
Output:
0 0 0
15 F 15
16 10 16
127 7F 127
128 81:0 128
255 81:7F 255
2097151 FF:FF:7F 2097151
2097152 81:80:80:0 2097152
Python
The vlq format is computed in a form for printing. This could easily be changed to a series of 8 bit ASCII chars whose integer value corresponds to the vlq for saving or transmission.
When transmitting the Vlq, octets are sent from the rightmost of the Vlq first.
<lang python>def tobits(n, _group=8, _sep='_', _pad=False):
'Express n as binary bits with separator'
bits = '{0:b}'.format(n)[::-1]
if _pad:
bits = '{0:0{1}b}'.format(n,
((_group+len(bits)-1)//_group)*_group)[::-1]
answer = _sep.join(bits[i:i+_group]
for i in range(0, len(bits), _group))[::-1]
answer = '0'*(len(_sep)-1) + answer
else:
answer = _sep.join(bits[i:i+_group]
for i in range(0, len(bits), _group))[::-1]
return answer
def tovlq(n):
return tobits(n, _group=7, _sep='1_', _pad=True)
def toint(vlq):
return int(.join(vlq.split('_1')), 2)
def vlqsend(vlq):
for i, byte in enumerate(vlq.split('_')[::-1]):
print('Sent byte {0:3}: {1:#04x}'.format(i, int(byte,2)))</lang>
Sample Output
The underscore separates groups of eight bits (octets), for readability
<lang python>>>> for n in (254, 255, 256, 257, -2+(1<<16), -1+(1<<16), 1<<16, 1+(1<<16), 0x200000, 0x1fffff ):
print('int: %7i bin: %26s vlq: %35s vlq->int: %7i' % (n, tobits(n,_pad=True), tovlq(n), toint(tovlq(n))))
int: 254 bin: 11111110 vlq: 00000001_11111110 vlq->int: 254
int: 255 bin: 11111111 vlq: 00000001_11111111 vlq->int: 255
int: 256 bin: 00000001_00000000 vlq: 00000010_10000000 vlq->int: 256
int: 257 bin: 00000001_00000001 vlq: 00000010_10000001 vlq->int: 257
int: 65534 bin: 11111111_11111110 vlq: 00000011_11111111_11111110 vlq->int: 65534
int: 65535 bin: 11111111_11111111 vlq: 00000011_11111111_11111111 vlq->int: 65535
int: 65536 bin: 00000001_00000000_00000000 vlq: 00000100_10000000_10000000 vlq->int: 65536
int: 65537 bin: 00000001_00000000_00000001 vlq: 00000100_10000000_10000001 vlq->int: 65537
int: 2097152 bin: 00100000_00000000_00000000 vlq: 00000001_10000000_10000000_10000000 vlq->int: 2097152
int: 2097151 bin: 00011111_11111111_11111111 vlq: 01111111_11111111_11111111 vlq->int: 2097151
>>> vlqsend(tovlq(0x200000))
Sent byte 0: 0x80
Sent byte 1: 0x80
Sent byte 2: 0x80
Sent byte 3: 0x01
>>> vlqsend(tovlq(0x1fffff))
Sent byte 0: 0xff
Sent byte 1: 0xff
Sent byte 2: 0x7f
>>> </lang>
REXX
<lang rexx> /*REXX program to test displaying of octets. */
num1=x2d(200000) ; say 'number1='num1 ' [in hex='d2x(num1)"]" num2=x2d(1fffff) ; say 'number2='num2 ' [in hex='d2x(num2)"]" num3=2097172 ; say 'number3='num3 ' [in hex='d2x(num3)"]" num4=2097151 ; say 'number4='num4 ' [in hex='d2x(num4)"]"
say
onum1=octet(num1) ; say 'number1 octet='onum1 onum2=octet(num2) ; say 'number2 octet='onum2 onum3=octet(num3) ; say 'number3 octet='onum3 onum4=octet(num4) ; say 'number4 octet='onum4
say
bnum1=x2d(space(onum1,0)) ; say 'number1='bnum1 bnum2=x2d(space(onum2,0)) ; say 'number2='bnum2 bnum3=x2d(space(onum3,0)) ; say 'number3='bnum3 bnum4=x2d(space(onum4,0)) ; say 'number4='bnum4
say
if num1==bnum1 &,
num2==bnum2 &,
num3==bnum3 &,
num4==bnum4 then say 'numbers are OK'
else say 'trouble in River City'
exit
octet: procedure; parse arg a,_; x=d2x(a) /*convert A to hex octet.*/
do j=length(x) by -2 to 1 /*process little end 1st.*/ _=substr(x,j-1,2,0) _ /*pad odd hexchars with a 0 on the left.*/ end
return _ </lang> Output:
number1=2097152 [in hex=200000] number2=2097151 [in hex=1FFFFF] number3=2097172 [in hex=200014] number4=2097151 [in hex=1FFFFF] number1 octet=20 00 00 number2 octet=1F FF FF number3 octet=20 00 14 number4 octet=1F FF FF number1=2097152 number2=2097151 number3=2097172 number4=2097151 numbers are OK
Tcl
<lang tcl>package require Tcl 8.5
proc vlqEncode number {
if {$number < 0} {error "negative not supported"}
while 1 {
lappend digits [expr {$number & 0x7f}] if {[set number [expr {$number >> 7}]] == 0} break
}
set out [format %c [lindex $digits 0]]
foreach digit [lrange $digits 1 end] {
set out [format %c%s [expr {0x80+$digit}] $out]
} return $out
} proc vlqDecode chars {
set n 0
foreach c [split $chars ""] {
scan $c %c c set n [expr {($n<<7) | ($c&0x7f)}] if {!($c&0x80)} break
} return $n
}</lang> Demo code: <lang tcl>proc numtohex {num} {
binary scan [string trimleft [binary format W $num] \0] H* hexEncoded regsub -all "..(?=.)" $hexEncoded "&:"
} proc strtohex {string} {
binary scan $string H* hexEncoded regsub -all "..(?=.)" $hexEncoded "&:"
} foreach testcase {
123 254 255 256 257 65534 65535 65536 65537 2097152 2097151 12345678901234566789
} {
set encoded [vlqEncode $testcase]
binary scan $encoded H* hexEncoded
regsub -all {..(?=.)} $hexEncoded &: hexEncoded
set decoded [vlqDecode $encoded]
puts "$testcase ([numtohex $testcase]) ==>\
[strtohex $encoded] ([string length $encoded] bytes) ==>\ $decoded" }</lang> Output:
123 (7b) ==> 7b (1 bytes) ==> 123 254 (fe) ==> 81:7e (2 bytes) ==> 254 255 (ff) ==> 81:7f (2 bytes) ==> 255 256 (01:00) ==> 82:00 (2 bytes) ==> 256 257 (01:01) ==> 82:01 (2 bytes) ==> 257 65534 (ff:fe) ==> 83:ff:7e (3 bytes) ==> 65534 65535 (ff:ff) ==> 83:ff:7f (3 bytes) ==> 65535 65536 (01:00:00) ==> 84:80:00 (3 bytes) ==> 65536 65537 (01:00:01) ==> 84:80:01 (3 bytes) ==> 65537 2097152 (20:00:00) ==> 81:80:80:00 (4 bytes) ==> 2097152 2097151 (1f:ff:ff) ==> ff:ff:7f (3 bytes) ==> 2097151 12345678901234566789 (ab:54:a9:8c:eb:1f:06:85) ==> 81:ab:aa:aa:b1:ce:d8:fc:8d:05 (10 bytes) ==> 12345678901234566789