Data commit

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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 7387c8f97b
commit cb5bb5e222
199093 changed files with 3378972 additions and 0 deletions

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---
from: http://rosettacode.org/wiki/Variable-length_quantity
note: Data Structures

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Implement some operations on [[wp:Variable-length quantity|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.
<br><br>

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F to_str(v)
R [ v.map(n -> hex(n).lowercase().zfill(2)).join( ) ]
F to_seq(UInt64 x)
V i = 0
L(ii) (9.<0).step(-1)
I x [&] (UInt64(127) << ii * 7) != 0
i = ii
L.break
[Byte] out
L(j) 0 .. i
out [+]= ((x >> ((i - j) * 7)) [&] 127) [|] 128
out[i] (+)= 128
R out
F from_seq(seq)
UInt64 r = 0
L(b) seq
r = (r << 7) [|] (b [&] 127)
R r
L(x) [UInt64(7'F), 40'00, 0, 003F'FFFE, 001F'FFFF, 0020'0000, 3311'A123'4DF3'1413]
V s = to_seq(x)
print(seq from hex(x).lowercase() to_str(s) back: hex(from_seq(s)).lowercase())

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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

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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;

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( ( 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
);

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#include <iomanip>
#include <iostream>
#include <vector>
std::ostream &operator<<(std::ostream &os, const std::vector<uint8_t> &v) {
auto it = v.cbegin();
auto end = v.cend();
os << "[ ";
if (it != end) {
os << std::setfill('0') << std::setw(2) << (uint32_t)*it;
it = std::next(it);
}
while (it != end) {
os << ' ' << std::setfill('0') << std::setw(2) << (uint32_t)*it;
it = std::next(it);
}
return os << " ]";
}
std::vector<uint8_t> to_seq(uint64_t x) {
int i;
for (i = 9; i > 0; i--) {
if (x & 127ULL << i * 7) {
break;
}
}
std::vector<uint8_t> out;
for (int j = 0; j <= i; j++) {
out.push_back(((x >> ((i - j) * 7)) & 127) | 128);
}
out[i] ^= 128;
return out;
}
uint64_t from_seq(const std::vector<uint8_t> &seq) {
uint64_t r = 0;
for (auto b : seq) {
r = (r << 7) | (b & 127);
}
return r;
}
int main() {
std::vector<uint64_t> src{ 0x7f, 0x4000, 0, 0x3ffffe, 0x1fffff, 0x200000, 0x3311a1234df31413ULL };
for (auto x : src) {
auto s = to_seq(x);
std::cout << std::hex;
std::cout << "seq from " << x << ' ' << s << " back: " << from_seq(s) << '\n';
std::cout << std::dec;
}
return 0;
}

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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();
}
}
}

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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...

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#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;
}

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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

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include "cowgol.coh";
sub VLQEncode(number: uint32, buf: [uint8]) is
var step := number;
while step > 0 loop
step := step >> 7;
buf := @next buf;
end loop;
var mark: uint8 := 0;
while number > 0 loop
buf := @prev buf;
[buf] := mark | (number as uint8 & 0x7F);
mark := 0x80;
number := number >> 7;
end loop;
end sub;
sub VLQDecode(buf: [uint8]): (result: uint32) is
result := 0;
loop
var byte := [buf];
buf := @next buf;
result := (result << 7) | (byte & 0x7F) as uint32;
if byte & 0x80 == 0 then
return;
end if;
end loop;
end sub;
sub VLQPrint(buf: [uint8]) is
loop
print_hex_i8([buf]);
if [buf] & 0x80 == 0 then
break;
end if;
buf := @next buf;
end loop;
end sub;
sub VLQTest(value: uint32) is
var buf: uint8[8];
print("Input: ");
print_hex_i32(value);
print_nl();
print("Encoded: ");
VLQEncode(value, &buf[0]);
VLQPrint(&buf[0]);
print_nl();
print("Decoded: ");
value := VLQDecode(&buf[0]);
print_hex_i32(value);
print_nl();
end sub;
VLQTest(0x200000);
print_nl();
VLQTest(0x1FFFFF);
print_nl();

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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));
}

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function NumberToVLQ(Num: int64): string;
{Convert Num to Variable-Length Quantity VLQ Octets (bytes)}
{Octet = 7-bit data and MSB indicating the last data item = 0 }
{Note: String are being used as byte-array because they are easy}
var I: integer;
var T: byte;
var BA: string;
begin
Result:='';
BA:='';
{Get array of octets}
while Num>0 do
begin
BA:=BA+char($7F and Num);
Num:=Num shr 7;
end;
{Reverse data and flag more data is coming}
Result:='';
for I:=Length(BA) downto 1 do
begin
T:=Byte(BA[I]);
if I<>1 then T:=T or $80;
Result:=Result+char(T);
end;
end;
function VLQToNumber(VLQ: string): int64;
{Convert Variable-Length Quantity VLQ Octets (bytes) to numbers}
{Octet = 7-bit data and MSB indicating the last data item = 0 }
{Note: String are being used as byte-array because they are easy}
var I: integer;
var T: byte;
var BA: string;
begin
Result:=0;
for I:=1 to Length(VLQ) do
Result:=(Result shl 7) or (Byte(VLQ[I]) and $7F);
end;
function VLQToString(VLQ: string): string;
{Convert VLQ to string of hex numbers}
var I: integer;
begin
Result:='(';
for I:=1 to Length(VLQ) do
begin
if I>1 then Result:=Result+', ';
Result:=Result+IntToHex(byte(VLQ[I]),2);
end;
Result:=Result+')';
end;
procedure ShowVLQ(Memo: TMemo; Num: int64);
var VLQ: string;
var I: int64;
var S: string;
begin
VLQ:=NumberToVLQ(Num);
S:=VLQToString(VLQ);
I:=VLQToNumber(VLQ);
Memo.Lines.Add('Original Number: '+Format('%x',[Num]));
Memo.Lines.Add('Converted to VLQ: '+Format('%s',[S]));
Memo.Lines.Add('Back to Original: '+Format('%x',[I]));
Memo.Lines.Add('');
end;
const Num1 = $0;
const Num2 = $7F;
const Num3 = $4000;
const Num4 = $1FFFFF;
const Num5 = $200000;
const Num6 = $3FFFFE;
const Num7 = $3311A1234DF31413;
procedure VariableLengthOctets(Memo: TMemo);
begin
ShowVLQ(Memo, Num1);
ShowVLQ(Memo, Num2);
ShowVLQ(Memo, Num3);
ShowVLQ(Memo, Num4);
ShowVLQ(Memo, Num5);
ShowVLQ(Memo, Num6);
ShowVLQ(Memo, Num7);
end;

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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

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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")
}
}

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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)
}
}

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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
}

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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]

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import Data.List (intercalate)
to :: Int -> Int -> [Int]
to _ 0 = []
to base i = to base q <> [r]
where
(q, r) = quotRem i base
from :: Int -> [Int] -> Int
from base = foldl1 ((+) . (base *))
--------------------------- TEST ---------------------------
main :: IO ()
main =
mapM_
(putStrLn .
intercalate " <-> " .
(((:) . (=<<) show . toBase) <*> (return . show . fromBase . toBase)))
[2097152, 2097151]
where
b = 8
fromBase = from b
toBase = to b

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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

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@ -0,0 +1,6 @@
N=: 128x
v2i=: (N&| N&#./.~ [: +/\ _1 |. N&>)@i.~&a.
i2v=: a. {~ [:;}.@(N+//.@,:N&#.inv)&.>
ifv=: v2i :. i2v
vfi=: i2v :. v2i
av=: 3 u: ]

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@ -0,0 +1,5 @@
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

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@ -0,0 +1,59 @@
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"));
}
}
}

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@ -0,0 +1,31 @@
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);
});

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@ -0,0 +1,46 @@
# "VARIABLE-LENGTH QUANTITY"
# A VLQ is a variable-length encoding of a number into a sequence of octets,
# with the most-significant octet first, and with the most significant bit first in each octet.
# The first (left-most) bit in each octet is a continuation bit: all octets except the last have the left-most bit set.
# The bits of the original number are taken 7 at a time from the right to form the octets.
# Thus, if the number is between 0 and 127, it is represented exactly as one byte.
# Produce a stream of the base $b "digits" of the input number,
# least significant first, with a final 0
def digits($b):
def mod: . % $b;
def div: ((. - mod) / $b);
recurse( select(. > 0) | div) | mod ;
# 2 <= $b <= 36
def tobase($b):
def digit: "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"[.:.+1];
if . == 0 then "0"
else [digits($b) | digit] | reverse[1:] | add
end;
# input: a decimal integer
# output: the corresponding variable-length quantity expressed as an array of strings of length 2,
# each representing an octet in hexadecimal notation, with most-significant octet first.
def vlq:
def lpad: if length == 2 then . else "0" + . end;
[digits(128) + 128] | reverse[1:] | .[-1] -=128 | map(tobase(16) | lpad);
# Input: a VLQ as produced by vlq/0
# Output: the corresponding decimal
def vlq2dec:
def x2d: # convert the character interpreted as a hex digit to a decimal
explode[0] as $x
| if $x < 65 then $x - 48 elif $x < 97 then $x - 55 else $x - 87 end;
map( ((.[0:1] | x2d) * 16) + (.[1:] | x2d) - 128)
| .[-1] += 128 # the most significant bit of the least significant octet
| reduce reverse[] as $x ({x: 0, m: 1}; .x += ($x * .m) | .m *= 128)
| .x ;
# The task
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
2097152, 2097151
| vlq as $vlq
| "\(lpad(8)) => \($vlq|join(",")|lpad(12)) => \($vlq | vlq2dec | lpad(8))"

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@ -0,0 +1,33 @@
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

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@ -0,0 +1,31 @@
// 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())}")
}
}

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@ -0,0 +1,7 @@
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}]

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@ -0,0 +1,22 @@
import strformat
proc toSeq(x: uint64): seq[uint8] =
var x = x
var f = 0u64
for i in countdown(9u64, 1):
if (x and 127'u64 shl (i * 7)) > 0:
f = i
break
for j in 0u64..f:
result.add uint8((x shr ((f - j) * 7)) and 127) or 128
result[f] = result[f] xor 128'u8
proc fromSeq(xs: openArray[uint8]): uint64 =
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 {x}: {c} back: {fromSeq(c)}"

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@ -0,0 +1,24 @@
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

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@ -0,0 +1,6 @@
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

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@ -0,0 +1,28 @@
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;

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@ -0,0 +1,30 @@
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;
}

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@ -0,0 +1,43 @@
-->
<span style="color: #008080;">function</span> <span style="color: #000000;">vlq_encode</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">msb</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">crash</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"unsigned integers only!"</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prepend</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">msb</span><span style="color: #0000FF;">+</span><span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">#7F</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">/</span><span style="color: #000000;">#80</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">msb</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#80</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">vlq_decode</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">si</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">*</span><span style="color: #000000;">#80</span><span style="color: #0000FF;">+</span><span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #004080;">byte</span><span style="color: #0000FF;">,</span><span style="color: #000000;">#7F</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">si</span><span style="color: #0000FF;">,</span><span style="color: #000000;">#80</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">svlg</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"#%02x:"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">testNumbers</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span> <span style="color: #000000;">#200000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">#1FFFFF</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">127</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">128</span> <span style="color: #0000FF;">}</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">vlq_encode</span><span style="color: #0000FF;">(</span><span style="color: #000000;">testNumbers</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">decoded</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">vlq_decode</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s -> %s -> %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">svlg</span><span style="color: #0000FF;">(</span><span style="color: #000000;">testNumbers</span><span style="color: #0000FF;">),</span><span style="color: #000000;">svlg</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">),</span><span style="color: #000000;">svlg</span><span style="color: #0000FF;">(</span><span style="color: #000000;">decoded</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">decoded</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">testNumbers</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">crash</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"something wrong"</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<!--

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@ -0,0 +1,14 @@
(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)) ) )

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@ -0,0 +1,23 @@
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)))

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>>> 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
>>>

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/*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($)

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#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))

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sub vlq_encode ($number is copy) {
my @vlq = (127 +& $number).fmt("%02X");
$number +>= 7;
while ($number) {
@vlq.push: (128 +| (127 +& $number)).fmt("%02X");
$number +>= 7;
}
@vlq.reverse.join: ':';
}
sub vlq_decode ($string) {
sum $string.split(':').reverse.map: {(:16($_) +& 127) +< (7 × $++)}
}
#test encoding and decoding
for (
0, 0xa, 123, 254, 255, 256,
257, 65534, 65535, 65536, 65537, 0x1fffff,
0x200000
) -> $testcase {
printf "%8s %12s %8s\n", $testcase,
my $encoded = vlq_encode($testcase),
vlq_decode($encoded);
}

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[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

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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
}
}

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$ 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;

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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))
}

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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
}

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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"
}

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Module Module1
Function ToVlq(v As ULong) As ULong
Dim array(8) As Byte
Dim buffer = ToVlqCollection(v).SkipWhile(Function(b) b = 0).Reverse().ToArray
buffer.CopyTo(array, 0)
Return BitConverter.ToUInt64(array, 0)
End Function
Function FromVlq(v As ULong) As ULong
Dim collection = BitConverter.GetBytes(v).Reverse()
Return FromVlqCollection(collection)
End Function
Iterator Function ToVlqCollection(v As ULong) As IEnumerable(Of Byte)
If v > Math.Pow(2, 56) Then
Throw New OverflowException("Integer exceeds max value.")
End If
Dim index = 7
Dim significantBitReached = False
Dim mask = &H7FUL << (index * 7)
While index >= 0
Dim buffer = mask And v
If buffer > 0 OrElse significantBitReached Then
significantBitReached = True
buffer >>= index * 7
If index > 0 Then
buffer = buffer Or &H80
End If
Yield buffer
End If
mask >>= 7
index -= 1
End While
End Function
Function FromVlqCollection(vlq As IEnumerable(Of Byte)) As ULong
Dim v = 0UL
Dim significantBitReached = False
Using enumerator = vlq.GetEnumerator
Dim index = 0
While enumerator.MoveNext
Dim buffer = enumerator.Current
If buffer > 0 OrElse significantBitReached Then
significantBitReached = True
v <<= 7
v = v Or (buffer And &H7FUL)
End If
index += 1
If index = 8 OrElse (significantBitReached AndAlso (buffer And &H80) <> &H80) Then
Exit While
End If
End While
End Using
Return v
End Function
Sub Main()
Dim values = {&H7FUL << 7 * 7, &H80, &H2000, &H3FFF, &H4000, &H200000, &H1FFFFF}
For Each original In values
Console.WriteLine("Original: 0x{0:X}", original)
REM collection
Dim seq = ToVlqCollection(original)
Console.WriteLine("Sequence: 0x{0}", seq.Select(Function(b) b.ToString("X2")).Aggregate(Function(a, b) String.Concat(a, b)))
Dim decoded = FromVlqCollection(seq)
Console.WriteLine("Decoded: 0x{0:X}", decoded)
REM ints
Dim encoded = ToVlq(original)
Console.WriteLine("Encoded: 0x{0:X}", encoded)
decoded = FromVlq(encoded)
Console.WriteLine("Decoded: 0x{0:X}", decoded)
Console.WriteLine()
Next
End Sub
End Module

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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))
}

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func OctIn(Dev); \Input from device value of sequence of octets
int Dev, N, Oct;
[N:= 0;
repeat Oct:= HexIn(Dev);
N:= N<<7 + (Oct&$7F);
until (Oct&$80) = 0;
return N;
];
proc OctOut(Dev, Num, Lev); \Output value to device as sequence of octets
int Dev, Num, Lev, Rem;
[Rem:= Num & $7F;
Num:= Num >> 7;
if Num # 0 then OctOut(Dev, Num, Lev+1);
if Lev > 0 then Rem:= Rem + $80;
SetHexDigits(2);
HexOut(Dev, Rem);
ChOut(Dev, ^ );
];
\Device 8 is a circular buffer that can be written and read back.
int N;
[for N:= 0 to $40_0000 do
[OctOut(8, N, 0);
if N # OctIn(8) then
[Text(0, "Error!"); exit];
];
OctOut(0, $1F_FFFF, 0); CrLf(0);
OctOut(0, $20_0000, 0); CrLf(0);
OctOut(0, $7F, 0); CrLf(0);
OctOut(0, $4000, 0); CrLf(0);
OctOut(0, 0, 0); CrLf(0);
OctOut(0, $3F_FFFE, 0); CrLf(0);
OctOut(0, $FFFF_FFFF, 0); CrLf(0);
]

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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

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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

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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) }

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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));