Variable-length quantity
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#
ANSI Standard BASIC
<lang ANSI BASIC>INPUT s$ LET s$ = LTRIM$(RTRIM$(s$)) LET v = 0 FOR i = 1 TO LEN(s$)
LET c$ = s$(i:i)
LET k = POS("0123456789abcdef", c$)
IF k > 0 THEN LET v = v*16 + k - 1
NEXT i PRINT "S= ";s$, "V=";v
! Convert back to hex LET hex$ ="0123456789abcdef" LET hs$=" "
FOR i = LEN(hs$) TO 1 STEP -1
IF v = 0 THEN EXIT FOR LET d = MOD(v, 16) + 1 LET hs$(i:i) = hex$(d:d) LET v = INT(v/16)
NEXT i PRINT hs$ END</lang> OUTPUT:
S= 200000 V= 2097152
200000
S= 1fffff V= 2097151
1fffff
Bracmat
Bracmat has no native octet array type. Luckily, the only octet that possibly can be zero in a VLQ is the last octet. Therefore a solitary VLQ can be expressed as a Bracmat string, which, just as a C string, is null terminated. If the last byte of the VLQ string has the high bit set, we know that the last octet contained 0-bits only. A problem is of course that VLQ's probably are meant to be concatenizable. With null bytes missing, this is no option for the VLQ's generated by this solution. <lang bracmat>( ( VLQ
= b07 b8 vlq
. 0:?b8
& :?vlq
& whl
' ( !arg:>0
& mod$(!arg.128):?b07
& (chr$(!b8+!b07)|) !vlq:?vlq
& 128:?b8
& div$(!arg.128):?arg
)
& str$!vlq
)
& ( NUM
= c num d
. 0:?num:?d
& whl
' ( @(!arg:%@?c ?arg)
& asc$!c:?c:~<128
& 128*(!c+-128+!num):?num
& 1+!d:?d
)
& (!c:<128&!c+!num:?num|)
& !num
)
& ( printVLQ
= c h
. :?h
& whl
' ( @(!arg:%@?c ?arg)
& d2x$(asc$!c):?x
& !h (@(!x:? [1)&0|) !x
: ?h
)
& ( asc$!c:~<128&!h 00:?h
|
)
& out$("VLQ :" str$!h)
)
& ( test
= vlq num
. out$("input:" !arg)
& VLQ$(x2d$!arg):?vlq
& printVLQ$!vlq
& NUM$!vlq:?num
& out$("back :" d2x$!num \n)
)
& test$200000 & test$1fffff & test$00 & test$7f & test$80 & test$81 & test$82 & test$894E410E0A );</lang> Output:
input: 200000 VLQ : 81808000 back : 200000 input: 1fffff VLQ : FFFF7F back : 1FFFFF input: 00 VLQ : back : 0 input: 7f VLQ : 7F back : 7F input: 80 VLQ : 8100 back : 80 input: 81 VLQ : 8101 back : 81 input: 82 VLQ : 8102 back : 82 input: 894E410E0A VLQ : 9194F2849C0A back : 894E410E0A
C
<lang c>#include <stdio.h>
- include <stdint.h>
void to_seq(uint64_t x, uint8_t *out) { int i, j; for (i = 9; i > 0; i--) { if (x & 127ULL << i * 7) break; } for (j = 0; j <= i; j++) out[j] = ((x >> ((i - j) * 7)) & 127) | 128;
out[i] ^= 128; }
uint64_t from_seq(uint8_t *in) { uint64_t r = 0;
do { r = (r << 7) | (uint64_t)(*in & 127); } while (*in++ & 128);
return r; }
int main() { uint8_t s[10]; uint64_t x[] = { 0x7f, 0x4000, 0, 0x3ffffe, 0x1fffff, 0x200000, 0x3311a1234df31413ULL};
int i, j; for (j = 0; j < sizeof(x)/8; j++) { to_seq(x[j], s); printf("seq from %llx: [ ", x[j]);
i = 0; do { printf("%02x ", s[i]); } while ((s[i++] & 128)); printf("] back: %llx\n", from_seq(s)); }
return 0; }</lang>output<lang>seq from 7f: [ 7f ] back: 7f seq from 4000: [ 81 80 00 ] back: 4000 seq from 0: [ 00 ] back: 0 seq from 3ffffe: [ 81 ff ff 7e ] back: 3ffffe seq from 1fffff: [ ff ff 7f ] back: 1fffff seq from 200000: [ 81 80 80 00 ] back: 200000 seq from 3311a1234df31413: [ b3 88 e8 a4 b4 ef cc a8 13 ] back: 3311a1234df31413</lang>
C#
For methods involving a BinaryReader or BinaryWriter please refer to this page. <lang csharp>namespace Vlq {
using System; using System.Collections.Generic; using System.Linq;
public static class VarLenQuantity
{
public static ulong ToVlq(ulong integer)
{
var array = new byte[8];
var buffer = ToVlqCollection(integer)
.SkipWhile(b => b == 0)
.Reverse()
.ToArray();
Array.Copy(buffer, array, buffer.Length);
return BitConverter.ToUInt64(array, 0);
}
public static ulong FromVlq(ulong integer)
{
var collection = BitConverter.GetBytes(integer).Reverse();
return FromVlqCollection(collection);
}
public static IEnumerable<byte> ToVlqCollection(ulong integer)
{
if (integer > Math.Pow(2, 56))
throw new OverflowException("Integer exceeds max value.");
var index = 7;
var significantBitReached = false;
var mask = 0x7fUL << (index * 7);
while (index >= 0)
{
var buffer = (mask & integer);
if (buffer > 0 || significantBitReached)
{
significantBitReached = true;
buffer >>= index * 7;
if (index > 0)
buffer |= 0x80;
yield return (byte)buffer;
}
mask >>= 7;
index--;
}
}
public static ulong FromVlqCollection(IEnumerable<byte> vlq)
{
ulong integer = 0;
var significantBitReached = false;
using (var enumerator = vlq.GetEnumerator())
{
int index = 0;
while (enumerator.MoveNext())
{
var buffer = enumerator.Current;
if (buffer > 0 || significantBitReached)
{
significantBitReached = true;
integer <<= 7;
integer |= (buffer & 0x7fUL);
}
if (++index == 8 || (significantBitReached && (buffer & 0x80) != 0x80))
break;
}
}
return integer;
}
public static void Main()
{
var integers = new ulong[] { 0x7fUL << 7 * 7, 0x80, 0x2000, 0x3FFF, 0x4000, 0x200000, 0x1fffff };
foreach (var original in integers)
{
Console.WriteLine("Original: 0x{0:X}", original);
//collection
var seq = ToVlqCollection(original);
Console.WriteLine("Sequence: 0x{0}", seq.Select(b => b.ToString("X2")).Aggregate(string.Concat));
var decoded = FromVlqCollection(seq);
Console.WriteLine("Decoded: 0x{0:X}", decoded);
//ints
var encoded = ToVlq(original);
Console.WriteLine("Encoded: 0x{0:X}", encoded);
decoded = FromVlq(encoded);
Console.WriteLine("Decoded: 0x{0:X}", decoded);
Console.WriteLine();
}
Console.WriteLine("Press any key to continue...");
Console.ReadKey();
}
}
}</lang>output<lang>Original: 0xFE000000000000 Sequence: 0xFF80808080808000 Decoded: 0xFE000000000000 Encoded: 0xFF80808080808000 Decoded: 0xFE000000000000
Original: 0x80 Sequence: 0x8100 Decoded: 0x80 Encoded: 0x8100 Decoded: 0x80
Original: 0x2000 Sequence: 0xC000 Decoded: 0x2000 Encoded: 0xC000 Decoded: 0x2000
Original: 0x3FFF Sequence: 0xFF7F Decoded: 0x3FFF Encoded: 0xFF7F Decoded: 0x3FFF
Original: 0x4000 Sequence: 0x818000 Decoded: 0x4000 Encoded: 0x818000 Decoded: 0x4000
Original: 0x200000 Sequence: 0x81808000 Decoded: 0x200000 Encoded: 0x81808000 Decoded: 0x200000
Original: 0x1FFFFF Sequence: 0xFFFF7F Decoded: 0x1FFFFF Encoded: 0xFFFF7F Decoded: 0x1FFFFF
Press any key to continue...</lang>
D
This implements a Variable-length Quantity struct for an ulong integer. <lang d>import std.stdio, std.string, std.file, std.algorithm;
/// Variable length quantity (unsigned long, max 63-bit). struct VLQ {
ulong value;
// This allows VLQ to work like an ulong. alias value this;
uint extract(in ubyte[] v) pure
in {
assert(v.length > 0);
} body {
immutable limit = min(v.length - 1, 8);
ulong t = 0;
size_t idx = 0;
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(in ubyte[] v) pure {
extract(v);
return this;
}
@property ubyte[] toVLQ() const pure {
ubyte[] v = [0x7f & value];
for (ulong k = value >>> 7; k > 0; k >>>= 7)
v ~= (k & 0x7f) | 0x80;
if (v.length > 9)
throw new Exception("Too large value.");
v.reverse();
return v;
}
static ulong[] split(in ubyte[] b) pure {
ulong[] res;
VLQ v;
for (size_t i = 0; i < b.length; ) {
i += v.extract(b[i .. $]);
res ~= v.value;
}
return res;
}
string toString() const pure /*nothrow*/ {
return format("(%(%02X:%))", this.toVLQ);
}
}
void main() { // VLQ demo code.
VLQ a = VLQ(0x7f),
b = VLQ(0x4000),
c;
writefln("a:%8x = %s\nb:%8x = %s\nc:%8x = %s",
a.value, a, b.value, b, c.value, c);
// Some operations. c = (a + 1) * b; a = c - 1; b = VLQ().from(a.toVLQ); a <<= 1;
// Convert ulong to octet sequence.
writefln("\na:%8x = %s\nb:%8x = %s\nc:%8x = %s",
a.value, a, b.value, b, c.value, c);
// Write them to a binary file.
std.file.write("vlqtest.bin", a.toVLQ ~ b.toVLQ ~ c.toVLQ);
// Read them back.
const buf = cast(ubyte[])std.file.read("vlqtest.bin");
writefln("\nFile length: %d bytes.", buf.length);
// Convert octet sequence to ulongs.
foreach (immutable i, immutable v; VLQ.split(buf))
writefln("%d:%8x = %s", i + 1, v, VLQ(v));
}</lang>
- Output:
a: 7f = (7F) b: 4000 = (81:80:00) c: 0 = (00) a: 3ffffe = (81:FF:FF:7E) b: 1fffff = (FF:FF:7F) c: 200000 = (81:80:80:00) File length: 11 bytes. 1: 3ffffe = (81:FF:FF:7E) 2: 1fffff = (FF:FF:7F) 3: 200000 = (81:80:80:00)
Erlang
This is built in.
7> binary:encode_unsigned(2097152). <<32,0,0>> 8> binary:decode_unsigned(<<32,0,0>>). 2097152 13> binary:encode_unsigned(16#1fffff). <<31,255,255>> 14> binary:decode_unsigned(<<31,255,255>>). 2097151
Euphoria
<lang euphoria>function vlq_encode(integer n)
sequence s
s = {}
while n > 0 do
s = prepend(s, #80 * (length(s) > 0) + and_bits(n, #7F))
n = floor(n / #80)
end while
if length(s) = 0 then
s = {0}
end if
return s
end function
function vlq_decode(sequence s)
integer n
n = 0
for i = 1 to length(s) do
n *= #80
n += and_bits(s[i], #7F)
if not and_bits(s[i], #80) then
exit
end if
end for
return n
end function
function svlg(sequence s)
sequence out
out = ""
for i = 1 to length(s) do
out &= sprintf("#%02x:", {s[i]})
end for
return out[1..$-1]
end function
constant testNumbers = { #200000, #1FFFFF, 1, 127, 128 } sequence s for i = 1 to length(testNumbers) do
s = vlq_encode(testNumbers[i])
printf(1, "#%02x -> %s -> #%02x\n", {testNumbers[i], svlg(s), vlq_decode(s)})
end for</lang>
Output:
#200000 -> #81:#80:#80:#00 -> #200000 #1FFFFF -> #FF:#FF:#7F -> #1FFFFF #01 -> #01 -> #01 #7F -> #7F -> #7F #80 -> #81:#00 -> #80
Go
Go has an implementation of variable length quantities in the standard library. <lang go>package main
import (
"fmt" "encoding/binary"
)
func main() {
buf := make([]byte, binary.MaxVarintLen64)
for _, x := range []int64{0x200000, 0x1fffff} {
v := buf[:binary.PutVarint(buf, x)]
fmt.Printf("%d encodes into %d bytes: %x\n", x, len(v), v)
x, _ = binary.Varint(v)
fmt.Println(x, "decoded")
}
}</lang> Output required by task:
2097152 encodes into 4 bytes: 80808002 2097152 decoded 2097151 encodes into 4 bytes: feffff01 2097151 decoded
More output showing negative numbers, the roll over from one byte to two, and larger numbers of different lengths:
0 encodes into 1 bytes: 00 0 decoded 1 encodes into 1 bytes: 02 1 decoded 2 encodes into 1 bytes: 04 2 decoded -1 encodes into 1 bytes: 01 -1 decoded -2 encodes into 1 bytes: 03 -2 decoded 63 encodes into 1 bytes: 7e 63 decoded 64 encodes into 2 bytes: 8001 64 decoded 589723405834 encodes into 6 bytes: 94b888e4a922 589723405834 decoded 3679899543542109203 encodes into 9 bytes: a6d098dfe9c8d09166 3679899543542109203 decoded
Groovy
Solution: <lang groovy>final RADIX = 7 final MASK = 2**RADIX - 1
def octetify = { n ->
def octets = []
for (def i = n; i != 0; i >>>= RADIX) {
octets << ((byte)((i & MASK) + (octets.empty ? 0 : MASK + 1)))
}
octets.reverse()
}
def deoctetify = { octets ->
octets.inject(0) { long n, octet ->
(n << RADIX) + ((int)(octet) & MASK)
}
}</lang>
Test (samples borrowed from Java example): <lang groovy>def testNumbers = [ 0x200000, 0x1fffff, 1, 127, 128, 589723405834L ]
testNumbers.each { a ->
def octets = octetify(a)
octets.each { printf "0x%02x ", it }; println ()
def a1 = deoctetify(octets)
assert a1 == a
}</lang>
Output:
0x81 0x80 0x80 0x00 0xff 0xff 0x7f 0x01 0x7f 0x81 0x00 0x91 0x94 0xf2 0x84 0x9c 0x0a
Haskell
<lang Haskell>import Numeric (readOct, showOct) import Data.List (intercalate)
to :: Int -> String to = flip showOct ""
from :: String -> Int from = fst . head . readOct
main :: IO () main =
mapM_
(putStrLn .
intercalate " <-> " . (pure (:) <*> to <*> (return . show . from . to)))
[2097152, 2097151]</lang>
Homemade Version:
<lang Haskell>import Data.List (intercalate)
to :: Int -> Int -> [Int] to _ 0 = [] to base i =
let go = to base in go (div i base) ++ [mod i base]
from :: Int -> [Int] -> Int from base = foldl1 ((+) . (base *))
main :: IO () main =
mapM_
(putStrLn .
intercalate " <-> " .
(((:) . (=<<) show . toBase) <*> (return . show . fromBase . toBase)))
[2097152, 2097151]
where
b = 8
fromBase = from b
toBase = to b</lang>
- Output:
10000000 <-> 2097152 7777777 <-> 2097151
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
JavaScript
Based on programmatic experimentation, it breaks at 2147483648 (2^31).
<lang javascript>const RADIX = 7; const MASK = 2**RADIX - 1;
const octetify = (n)=> { if (n >= 2147483648) { throw new RangeError("Variable Length Quantity not supported for numbers >= 2147483648"); } const octets = []; for (let i = n; i != 0; i >>>= RADIX) { octets.push((((i & MASK) + (octets.empty ? 0 : (MASK + 1))))); } octets.reverse(); return octets; };
const deoctetify = (octets)=> octets.reduce((n, octet)=> (n << RADIX) + (octet & MASK) , 0);
// Test (assuming Node.js)
const assert = require("assert"); const testNumbers = [ 0x200000, 0x1fffff, 1, 127, 128, 2147483647 /*, 589723405834*/ ]
testNumbers.forEach((number)=> { const octets = octetify(number) console.log(octets); const got_back_number = deoctetify(octets) assert.strictEqual(got_back_number, number); });</lang>
Julia
<lang julia>using Printf
mutable struct VLQ
quant::Vector{UInt8}
end
function VLQ(n::T) where T <: Integer
quant = UInt8.(digits(n, 128)) @inbounds for i in 2:length(quant) quant[i] |= 0x80 end VLQ(reverse(quant))
end
import Base.UInt64 function Base.UInt64(vlq::VLQ)
quant = reverse(vlq.quant)
n = shift!(quant)
p = one(UInt64)
for i in quant
p *= 0x80
n += p * ( i & 0x7f)
end
return n
end
const test = [0x00200000, 0x001fffff, 0x00000000, 0x0000007f,
0x00000080, 0x00002000, 0x00003fff, 0x00004000,
0x08000000, 0x0fffffff]
for i in test
vlq = VLQ(i)
j = UInt(vlq)
@printf "0x%-8x => [%-25s] => 0x%x\n" i join(("0x" * hex(r, 2) for r in vlq.quant), ", ") j
end</lang>
- Output:
0x200000 => [0x81, 0x80, 0x80, 0x00 ] => 0x200000 0x1fffff => [0xff, 0xff, 0x7f ] => 0x1fffff 0x0 => [0x00 ] => 0x0 0x7f => [0x7f ] => 0x7f 0x80 => [0x81, 0x00 ] => 0x80 0x2000 => [0xc0, 0x00 ] => 0x2000 0x3fff => [0xff, 0x7f ] => 0x3fff 0x4000 => [0x81, 0x80, 0x00 ] => 0x4000 0x8000000 => [0xc0, 0x80, 0x80, 0x00 ] => 0x8000000 0xfffffff => [0xff, 0xff, 0xff, 0x7f ] => 0xfffffff
Kotlin
<lang scala>// version 1.0.6
fun Int.toOctets(): ByteArray {
var s = Integer.toBinaryString(this)
val r = s.length % 7
var z = s.length / 7
if (r > 0) {
z++
s = s.padStart(z * 7, '0')
}
s = Array(z) { "1" + s.slice(it * 7 until (it + 1) * 7) }.joinToString("")
s = s.take(s.length - 8) + "0" + s.takeLast(7)
return ByteArray(z) { Integer.parseInt(s.slice(it * 8 until (it + 1) * 8), 2).toByte() }
}
fun ByteArray.fromOctets(): Int {
var s = "" for (b in this) s += Integer.toBinaryString(b.toInt()).padStart(7, '0').takeLast(7) return Integer.parseInt(s, 2)
}
fun main(args: Array<String>) {
val tests = intArrayOf(0x7f, 0x3fff, 0x200000, 0x1fffff)
for (test in tests) {
val ba = test.toOctets()
print("${"0x%x".format(test).padEnd(8)} -> ")
var s = ""
ba.forEach { s += "0x%02x ".format(it) }
println("${s.padEnd(20)} <- ${"0x%x".format(ba.fromOctets())}")
}
}</lang>
- Output:
0x7f -> 0x7f <- 0x7f 0x3fff -> 0xff 0x7f <- 0x3fff 0x200000 -> 0x81 0x80 0x80 0x00 <- 0x200000 0x1fffff -> 0xff 0xff 0x7f <- 0x1fffff
LiveCode
This task was completed a different (and better) way a long time ago in UDI's PMD/MakeSMF Lib for LiveCode (back when it was MetaCard). Here is my own (and probably slower) version. -- Paul McClernan
<lang LiveCode> on DecToVLQ
Ask "Enter base 10 value:" -- input dialog box
if it is not empty then
if it is a number then
put it into theString
if isWholeNumString(theString) is false then -- I think there is built in equivalent for this but I rolled my own!
answer "Only Whole Decimal Numbers Are Allowed!"
exit DecToVLQ
end if
if theString>4294967295 then
answer "This function fails with whole numbers over 4294967295!"&cr\
& "4294967295 is the maximum allowed value for 32bits (4 bytes)"
exit DecToVLQ
end if
if theString>268435455 then
answer "This function is not accurate with whole numbers over 268435455!"&cr\
& "268435455 is the maximum allowed value for 28bit (7bits per byte) MIDI delta-time VLQ"
end if
put "Original Whole Number="& theString & cr & \
"Original Whole Number in Hex="& baseConvert(theString,10,16) & cr & \ --- LC's built in baseConvert function
"Variable Length Quantity in Hex=" & wholeNumToVLQ(theString) into fld "Output"
else
answer "Only Whole Decimal Numbers Are Allowed!"
end if
end if
end DecToVLQ
function wholeNumToVLQ theWholeNum
-- baseConvert(number,originalBase,destinationBase) -- there is also bitwise operations in LC but I took the long road
if theWholeNum < 127 then -- if it fits into a single 7bit byte value and theres no need to process it
put baseConvert(theWholeNum,10,16) into VQLinHex
if the number of chars in VQLinHex=1 then put "0" before VQLinHex
return VQLinHex
exit wholeNumToVLQ
end if
put baseConvert(theWholeNum,10,2) into theBits
put number of chars in theBits into x
put 0 into bitCounter
put empty into the7bitBytes
repeat
if char x of theBits is not empty then
put char x theBits before the7bitBytes
delete char x of theBits
if theBits is empty then exit repeat
put number of chars in theBits into x
add 1 to bitCounter
if bitCounter=7 then
put "," before the7bitBytes
put 0 into bitCounter
next repeat
end if
else
exit repeat
end if
end repeat
get the number of chars in item 1 of the7bitBytes
if it<7 then
put 7 - it into x
repeat x
put "0" before item 1 of the7bitBytes
end repeat
end if
put the number of items in the7bitBytes into y
repeat with x = 1 to y
if x is not y then
put "1" before item x of the7bitBytes
else
put "0" before item x of the7bitBytes
end if
put baseConvert(item x of the7bitBytes,2,16) into item x of the7bitBytes
if the number of chars in item x of the7bitBytes<2 then put "0" before item x of the7bitBytes
put item x of the7bitBytes after VQLinHex
end repeat
return VQLinHex
end wholeNumToVLQ
function isWholeNumString theString
put the number of chars in theString into y
repeat with x = 1 to y
if char x of theString is not in "0123456789" then
return false
exit isWholeNumString
end if
end repeat
return true
end isWholeNumString </lang>
- Output:
Original Whole Number=2097152 Original Whole Number in Hex=200000 Variable Length Quantity in Hex=81808000
Convert back:
<lang LiveCode> function VLQtoWholeNum theHexVLQ
-- The number must be an integer between zero and 4,294,967,295
put baseConvert(theHexVLQ,16,2) into theBits
put 0 into bitCounter
put empty into the8bitBytes
repeat
if char 1 of theBits is not empty then
put char 1 theBits after the8bitBytes
delete char 1 of theBits
if theBits is empty then exit repeat
add 1 to bitCounter
if bitCounter=8 then
put "," after the8bitBytes
put 0 into bitCounter
next repeat
end if
else
exit repeat
end if
end repeat
put the number of items in the8bitBytes into y
repeat with x = 1 to y
put char 1 of item x of the8bitBytes into lengthCntrlBit
delete char 1 of item x of the8bitBytes
if the number of chars in item x of the8bitBytes < 7 then
repeat 7 - (the number of chars in item x of the8bitBytes)
put "0" before item x of the8bitBytes
end repeat
end if
put item x of the8bitBytes after WholeNumInBinary
switch lengthCntrlBit
case "1"
next repeat
break
case "0"
exit repeat
break
end switch
end repeat
return baseConvert(WholeNumInBinary,2,10)
end VLQtoWholeNum
function isHexString theString
---again there is probably an easier way to do this:
if char 1 to 2 of theString is "0x" then delete char 1 to 2 of theString
put the number of chars in theString into y
repeat with x = 1 to y
if char x of theString is not in "abcdefABCDEF0123456789" then
return false
end if
end repeat
end isHexString
on VLQHexToWholeNum
Ask "Enter Variable Length Quantity Hex Value:" -- input dialog
if it is not empty then
if char 1 to 2 of it is "0x" then delete char 1 to 2 of it
put it into hexString
if isHexString(hexString) is false then
answer "Only Valid Hex Digits Are Allowed!"
exit VLQHexToWholeNum
else
put "Original Variable Length Quantity in Hex="& hexString & cr & \
"Whole Number=" & VLQtoWholeNum(hexString) into fld "Output"
end if
end if
end VLQHexToWholeNum </lang>
- Output:
Original Variable Length Quantity in Hex=FFFF7F Whole Number=2097151
Mathematica
<lang Mathematica>toOctets[n_Integer] :=
StringJoin @@@
Partition[
PadLeft[Characters@IntegerString[n, 16],
2 Ceiling[Plus @@ DigitCount[n, 16]/2], {"0"}], 2]
fromOctets[octets_List] := FromDigits[StringJoin @@ octets, 16]
Grid[{#, toOctets@#, fromOctets[toOctets@#]} & /@ {16^^3ffffe,
16^^1fffff, 16^^200000}]</lang>
- Output:
4194302 {3f,ff,fe} 4194302 2097151 {1f,ff,ff} 2097151 2097152 {20,00,00} 2097152
Nim
<lang nim>import unsigned, strutils
proc toSeq(x: uint64): seq[uint8] =
var x = x
result = @[]
var f = 0
for i in countdown(9, 1):
if (x and (127'u64 shl uint((i * 7)))) > 0'u64:
f = i
break
for j in 0..f:
result.add(uint8((x shr uint64((f - j) * 7)) and 127) or 128)
result[f] = result[f] xor 128'u8
proc fromSeq(xs): uint64 =
result = 0 for x in xs: result = (result shl 7) or (x and 127)
for x in [0x7f'u64, 0x4000'u64, 0'u64, 0x3ffffe'u64, 0x1fffff'u64,
0x200000'u64, 0x3311a1234df31413'u64]: let c = toSeq(x) echo "seq from $#: $# back: $#".format(x, c, fromSeq(c))</lang>
Output:
seq from 127: @[127] back: 127 seq from 16384: @[129, 128, 0] back: 16384 seq from 0: @[0] back: 0 seq from 4194302: @[129, 255, 255, 126] back: 4194302 seq from 2097151: @[255, 255, 127] back: 2097151 seq from 2097152: @[129, 128, 128, 0] back: 2097152 seq from 3679899543542109203: @[179, 136, 232, 164, 180, 239, 204, 168, 19] back: 3679899543542109203
OCaml
<lang ocaml>let to_vlq n =
let a, b = n lsr 7, n land 0x7F in let rec aux n acc = let x = (n land 0x7F) lor 0x80 and xs = n lsr 7 in if xs > 0 then aux xs (x::acc) else x::acc in aux a [b]
let to_num = List.fold_left (fun n x -> n lsl 7 + (x land 0x7F)) 0
let v_rep n =
Printf.printf "%d ->" n; let seq = to_vlq n in List.iter (Printf.printf " 0x%02X") seq; 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 -> 0x81 0x80 0x80 0x00 -> 2097152 2097151 -> 0xFF 0xFF 0x7F -> 2097151
PARI/GP
<lang parigp>hex(s)=my(a=10,b=11,c=12,d=13,e=14,f=15);subst(Pol(eval(Vec(s))),'x,16); n1=hex("200000");n2=hex("1fffff"); v1=digits(n1,256) v2=digits(n2,256) subst(Pol(v1),'x,256)==n1 subst(Pol(v2),'x,256)==n2</lang>
- Output:
%1 = [32, 0, 0] %2 = [31, 255, 255] %3 = 1 %4 = 1
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' . $num;
} </lang>
Output:
0 00 0
10 0a 10
123 7b 123
254 81:7e 254
255 81:7f 255
256 82:00 256
257 82:01 257
65534 83:ff:7e 65534
65535 83:ff:7f 65535
65536 84:80:00 65536
65537 84:80:01 65537
2097151 ff:ff:7f 2097151
2097152 81:80:80:00 2097152
Phix
Copy of Euphoria, modified to pack several numbers into a single stream. Also added an explicit check that (as per wp) only unsigned numbers are attempted. <lang Phix>function vlq_encode(sequence s) sequence res = {} integer n, msb
for i=length(s) to 1 by -1 do
n = s[i]
if n<0 then crash("unsigned integers only!") end if
msb = 0
while 1 do
res = prepend(res,msb+and_bits(n,#7F))
n = floor(n/#80)
if n=0 then exit end if
msb = #80
end while
end for
return res
end function
function vlq_decode(sequence s) sequence res = {} integer n = 0, byte
for i=1 to length(s) do
byte = s[i]
n = n*#80+and_bits(byte,#7F)
if not and_bits(byte,#80) then
res = append(res,n)
n = 0
end if
end for
return res
end function
function svlg(sequence s) string res = ""
for i=1 to length(s) do
res &= sprintf("#%02x:",{s[i]})
end for
return res[1..$-1]
end function
constant testNumbers = { #200000, #1FFFFF, 1, 127, 128 } sequence s = vlq_encode(testNumbers) sequence decoded = vlq_decode(s) printf(1,"%s -> %s -> %s\n",{svlg(testNumbers),svlg(s),svlg(decoded)}) if decoded!=testNumbers then crash("something wrong") end if</lang>
- Output:
#200000:#1FFFFF:#01:#7F:#80 -> #81:#80:#80:#00:#FF:#FF:#7F:#01:#7F:#81:#00 -> #200000:#1FFFFF:#01:#7F:#80
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
PL/I
<lang PL/I> test: procedure options(main);
declare s character (20) varying; declare c character (1); declare v fixed binary (31); declare (i, k) fixed binary;
get edit (s) (L);
s = trim (s);
v = 0;
do i = 1 to length(s);
c = substr(s, i, 1);
k = index('0123456789abcdef', c);
if k > 0 then v = v*16 + k - 1;
end;
put skip data (s, v);
/* Convert back to hex */
declare hex character(16) initial ('0123456789abcdef');
declare hs character (20) initial ();
declare d fixed binary;
do i = length(hs) to 1 by -1 until (v = 0);
d = mod(v, 16) + 1;
substr(hs, i, 1) = substr(hex, d, 1);
v = v/16;
end;
put skip list (hs);
end test; </lang> OUTPUT:
S='200000' V= 2097152;
200000
S='1fffff' V= 2097151;
1fffff
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>
Racket
<lang Racket>
- lang racket
(define (try n)
(printf "Original number: ~s (0x~x)\n" n n)
(define 4octets (integer->integer-bytes n 4 #f))
(printf "Octets: ~a (byte-string: ~s)\n"
(string-join (map (λ(o) (~r o #:base 16))
(bytes->list 4octets))
":")
4octets)
(define m (integer-bytes->integer 4octets #f))
(printf "Back to a number: ~s (~a)\n"
m (if (= m n) "OK" "BAD")))
(for-each try '(#x200000 #x1fffff)) </lang>
Output:
Original number: 2097152 (0x200000) Octets: 0:0:20:0 (byte-string: #"\0\0 \0") Back to a number: 2097152 (OK) Original number: 2097151 (0x1fffff) Octets: ff:ff:1f:0 (byte-string: #"\377\377\37\0") Back to a number: 2097151 (OK)
Raku
(formerly 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
REXX
<lang rexx>/*REXX program displays (and also tests/verifies) some numbers as octets. */ nums = x2d(200000) x2d(1fffff) 2097172 2097151
- =words(nums)
say ' number hex octet original' say '══════════ ══════════ ══════════ ══════════' ok=1
do j=1 for #; @.j= word(nums,j)
onum.j=octet(@.j)
orig.j= x2d( space(onum.j, 0) )
w=10
say center(@.j, w) center(d2x(@.j), w) center(onum.j, w) center(orig.j, w)
if @.j\==orig.j then ok=0
end /*j*/
say if ok then say 'All ' # " numbers are OK." /*all of the numbers are good. */
else say "Some numbers are not OK." /*some of the numbers are ¬good. */
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ octet: procedure; parse arg z,$ /*obtain Z from the passed arguments.*/
x=d2x(z) /*convert Z to a hexadecimal octet. */
do j=length(x) by -2 to 1 /*process the "little" end first. */
$= substr(x, j-1, 2, 0) $ /*pad odd hexadecimal characters with */
end /*j*/ /* ··· a zero on the left. */
return strip($)</lang>
- output when using the default input:
number hex octet original ══════════ ══════════ ══════════ ══════════ 2097152 200000 20 00 00 2097152 2097151 1FFFFF 1F FF FF 2097151 2097172 200014 20 00 14 2097172 2097151 1FFFFF 1F FF FF 2097151 All 4 numbers are OK.
Ruby
Array#pack can encode the BER-compressed integer, which is identical to the variable-length quantity from the MIDI specification. String#unpack can decode it.
<lang ruby>[0x200000, 0x1fffff].each do |i|
# Encode i => BER
ber = [i].pack("w")
hex = ber.unpack("C*").collect {|c| "%02x" % c}.join(":")
printf "%s => %s\n", i, hex
# Decode BER => j
j = ber.unpack("w").first
i == j or fail "BER not preserve integer"
end</lang>
2097152 => 81:80:80:00 2097151 => ff:ff:7f
Scala
<lang scala>object VlqCode {
def encode(x:Long)={
val result=scala.collection.mutable.Stack[Byte]()
result push (x&0x7f).toByte
var l = x >>> 7
while(l>0){
result push ((l&0x7f)|0x80).toByte
l >>>= 7
}
result.toArray
}
def decode(a:Array[Byte])=a.foldLeft(0L)((r, b) => r<<7|b&0x7f)
def toString(a:Array[Byte])=a map("%02x".format(_)) mkString("[", ", ", "]")
def test(x:Long)={
val enc=encode(x)
println("0x%x => %s => 0x%x".format(x, toString(enc), decode(enc)))
}
def main(args: Array[String]): Unit = {
val xs=Seq(0, 0x7f, 0x80, 0x2000, 0x3fff, 0x4000, 0x1FFFFF, 0x200000, 0x8000000,
0xFFFFFFF, 0xFFFFFFFFL, 0x842FFFFFFFFL, 0x0FFFFFFFFFFFFFFFL)
xs foreach test
}
}</lang> Output:
0x0 => [00] => 0x0 0x7f => [7f] => 0x7f 0x80 => [81, 00] => 0x80 0x2000 => [c0, 00] => 0x2000 0x3fff => [ff, 7f] => 0x3fff 0x4000 => [81, 80, 00] => 0x4000 0x1fffff => [ff, ff, 7f] => 0x1fffff 0x200000 => [81, 80, 80, 00] => 0x200000 0x8000000 => [c0, 80, 80, 00] => 0x8000000 0xfffffff => [ff, ff, ff, 7f] => 0xfffffff 0xffffffff => [8f, ff, ff, ff, 7f] => 0xffffffff 0x842ffffffff => [82, 88, af, ff, ff, ff, 7f] => 0x842ffffffff 0xfffffffffffffff => [8f, ff, ff, ff, ff, ff, ff, ff, 7f] => 0xfffffffffffffff
Seed7
The example below uses bigInteger numbers, since variable-length quantities are able to represent integer numbers of unlimited size. <lang seed7>$ include "seed7_05.s7i";
include "bigint.s7i";
const func string: toSequence (in var bigInteger: number) is func
result
var string: sequence is "";
begin
sequence := str(chr(ord(number mod 128_)));
number >>:= 7;
while number <> 0_ do
sequence := str(chr(ord(number mod 128_) + 128)) & sequence;
number >>:= 7;
end while;
end func;
const func bigInteger: fromSequence (in string: sequence) is func
result
var bigInteger: number is 0_;
local
var integer: index is 1;
begin
while ord(sequence[index]) >= 128 do
number <<:= 7;
number +:= bigInteger conv (ord(sequence[index]) - 128);
incr(index);
end while;
number <<:= 7;
number +:= bigInteger conv ord(sequence[index]);
end func;
const proc: main is func
local
const array bigInteger: testValues is [] (
0_, 10_, 123_, 254_, 255_, 256_, 257_, 65534_, 65535_, 65536_, 65537_, 2097151_, 2097152_);
var string: sequence is "";
var bigInteger: testValue is 0_;
var char: element is ' ';
begin
for testValue range testValues do
sequence := toSequence(testValue);
write("sequence from " <& testValue <& ": [ ");
for element range sequence do
write(ord(element) radix 16 lpad0 2 <& " ");
end for;
writeln("] back: " <& fromSequence(sequence));
end for;
end func;</lang>
Output:
sequence from 0: [ 00 ] back: 0 sequence from 10: [ 0a ] back: 10 sequence from 123: [ 7b ] back: 123 sequence from 254: [ 81 7e ] back: 254 sequence from 255: [ 81 7f ] back: 255 sequence from 256: [ 82 00 ] back: 256 sequence from 257: [ 82 01 ] back: 257 sequence from 65534: [ 83 ff 7e ] back: 65534 sequence from 65535: [ 83 ff 7f ] back: 65535 sequence from 65536: [ 84 80 00 ] back: 65536 sequence from 65537: [ 84 80 01 ] back: 65537 sequence from 2097151: [ ff ff 7f ] back: 2097151 sequence from 2097152: [ 81 80 80 00 ] back: 2097152
Sidef
<lang ruby>func vlq_encode(num) {
var t = (0x7F & num)
var str = t.chr
while (num >>= 7) {
t = (0x7F & num)
str += chr(0x80 | t)
}
str.reverse
}
func vlq_decode(str) {
var num =
str.each_byte { |b|
num += ('%07b' % (b & 0x7F))
}
Num(num, 2)
}
var tests = [0, 0xa, 123, 254, 255, 256,
257, 65534, 65535, 65536, 65537, 0x1fffff,
0x200000]
tests.each { |t|
var vlq = vlq_encode(t)
printf("%8s %12s %8s\n", t,
vlq.bytes.join(':', { "%02X" % _ }), vlq_decode(vlq))
}</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
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
TXR
TXR's carray type, closely associated with the Foreign Function Interface, has functions for converting between integers and foreign arrays. The arrays can use any element type. The integer is stored in big endian order, and "right justified" within the buffer, so that its least significant byte is aligned with the least significant byte of the last element of the array.
Two representations are supported: unsigned and signed. The unsigned representation takes only non-negative integers. It is a straightforward pure binary enumeration. The signed representation uses twos complement. The most significant byte of the array representation is in the range 80-FF if the value is negative, otherwise in the range 0 to 7F. This means that in some cases, a zero byte has to be added.
Interactive session:
1> (carray-num #x200000) #<carray 3 #<ffi-type uchar>> 2> (carray-get *1) #(32 0 0) 3> (carray-num #x1FFFFF) #<carray 3 #<ffi-type uchar>> 4> (carray-get *3) #(31 255 255) 5> (num-carray *1) 2097152 6> (num-carray *3) 2097151
Conversion to a carray not based on the default uchar:
1> (carray-num #x123456789 (ffi uint32)) #<carray 2 #<ffi-type uint32>> 2> (carray-get *1) #(16777216 2305246499)
This number requires two 32-bit units to store. Because uint32 is in the native endian, opposite to the big endian storage of the integer, the words come out byte swapped. The be-uint32 type could be used to change this.
Wren
<lang ecmascript>import "/fmt" for Fmt, Conv import "/str" for Str
var toOctets = Fn.new { |n|
var s = Conv.itoa(n, 2)
var le = s.count
var r = le % 7
var d = (le/7).floor
if (r > 0) {
d = d + 1
s = Fmt.zfill(7 * d, s)
}
var chunks = Str.chunks(s, 7)
var last = "0" + chunks[-1]
s = chunks[0..-2].map { |ch| "1" + ch }.join() + last
return Str.chunks(s, 8).map { |ch| Conv.atoi(ch, 2) }.toList
}
var fromOctets = Fn.new { |octets|
var s = ""
for (oct in octets) {
var bin = Conv.itoa(oct, 2)
bin = Fmt.zfill(7, bin)
s = s + bin[-7..-1]
}
return Conv.atoi(s, 2)
}
var tests = [2097152, 2097151] for (test in tests) {
var octets = toOctets.call(test)
var display = octets.map { |oct| "Ox" + Fmt.xz(2, oct) }.toList
System.write("%(test) -> %(Fmt.v("s", 4, display, 0, " ", "")) -> ")
System.print(fromOctets.call(octets))
}</lang>
- Output:
2097152 -> Ox81 Ox80 Ox80 Ox00 -> 2097152 2097151 -> Oxff Oxff Ox7f -> 2097151
zkl
<lang zkl>fcn to_seq(x){ //--> list of ints
z:=(x.log2()/7);
(0).pump(z+1,List,'wrap(j){
x.shiftRight((z-j)*7).bitAnd(0x7f).bitOr((j!=z) and 0x80 or 0)
});
}
fcn from_seq(in){ in.reduce(fcn(p,n){ p.shiftLeft(7).bitOr(n.bitAnd(0x7f)) },0) }</lang> <lang zkl>ns:=T(0x7f, 0x4000, 0, 0x3ffffe, 0x1fffff, 0x200000, 0x3311a1234df31413); ms:=ns.apply(to_seq); ns.zipWith(fcn{"%8,x --> %s --> %,x".fmt(vm.arglist.xplode()).println()},
ms.apply("apply","%,x".fmt),
ms.apply(from_seq));</lang>
- Output:
7f --> L("7f") --> 7f
40|00 --> L("81","80","0") --> 40|00
0 --> L("0") --> 0
3f|ff|fe --> L("81","ff","ff","7e") --> 3f|ff|fe
1f|ff|ff --> L("ff","ff","7f") --> 1f|ff|ff
20|00|00 --> L("81","80","80","0") --> 20|00|00
33|11|a1|23|4d|f3|14|13 --> L("b3","88","e8","a4","b4","ef","cc","a8","13")
--> 33|11|a1|23|4d|f3|14|13
Note: the strings in the output are numbers formatted to hex (ie to_seq returns a list of ints). A "|" is used between bytes for ease of reading.