I have a 16-bit in a string but this is the representation of a signed number. Is there a way/function that do the converson from signed bits to decimal ?
The function tonumber() assumes the bits are unsigned.
Lua 5.3/5.4
Use string.unpack with a format string <i2 to read the binary string. (use >i2 for big endian data)
--0x8000 ---> -32768
local v = string.unpack('<i2', '\x00\x80')
Lua 5.2/5.1
There is no string.unpack, so you have to read each byte of the string, then compute the value manually.
local l, h = string.byte('\x00\x80', 1, 2)
local v = h * 256 + l --big endian: v = l * 256 + h
if v > 32767 then v = v - 65536 end
byte 0: min_value (0-3 bit)
max_value (4-7 bit)
The byte0 should be the min and max values combined.
min and max values are both integers (in 0-15 range).
I should convert them into 4-bit binary, and combine them somehow? (how?)
E.g.
min_value=2 // 0010
max_value=3 // 0011
The result should be an Uint8, and the value: 00100011
You can use the shift left operator << to get the result you want:
result = ((min_value << 4) + max_value).toRadixString(2).padLeft(8, '0');
I want to convert an integer from 0 to 65355 and for that I need a two byte representation. I'm trying to divide it by 2, 8 times, and sum the powers of 2 when the rest is one, and then cast that integer as a byte but I'm having problems meeting the restrictions of a byte (256). The second byte will be the rest of the 8th division and I'm having problems casting that as a byte too.
The following is my code for the previously described function method:
method convertBin(i:int) returns (b:seq<byte>)
requires 0<=i<=65535;
{
var b1:=0;
var q:=i;
var j:=0;
while j<8
invariant 0<=j<=8 && (b1 as int)< power(2,j)
decreases 8-j
{
var p:int;
if(q%2==1){
p:=power(2, j);
b1:=b1 + p;
q:=q/2;
}
j:=j+1;
}
b1:=b1 as byte;
b:=[b1]+[q as byte];
}
To complete your example, you need stronger loop invariants. But you don't need a loop at all, since there's no reason to divide only by 2.
Here's doing it with byte as a subset type:
type byte = x | 0 <= x < 256
method convertBin(i: int) returns (b1: byte, b0: byte)
requires 0 <= i < 0x1_0000
ensures i == 256 * b1 + b0
{
b1, b0 := i / 256, i % 256;
}
And here's the same program, but with byte being a newtype:
newtype byte = x | 0 <= x < 256
method convertBin(i: int) returns (b1: byte, b0: byte)
requires 0 <= i < 0x1_0000
ensures i == 256 * b1 as int + b0 as int
{
b1, b0 := (i / 256) as byte, (i % 256) as byte;
}
Rustan
I am using Lua on Redis and want to compare two signed 64-bit numbers, which are stored in two 8-byte/character strings.
How can I compare them using the libraries available in Redis?
http://redis.io/commands/EVAL#available-libraries
I'd like to know >/< and == checks. I think this probably involves pulling two 32-bit numbers for each 64-bit int, and doing some clever math on those, but I am not sure.
I have some code to make this less abstract. a0, a1, b0, b1 are all 32 bit numbers used to represent the msb & lsb's of two 64-bit signed int 64s:
-- ...
local comp_int64s = function (a0, a1, b0, b1)
local cmpres = 0
-- TOOD: Real comparison
return cmpres
end
local l, a0, a1, b0, b1
a0, l = bit.tobit(struct.unpack("I4", ARGV[1]))
a1, l = bit.tobit(struct.unpack("I4", ARGV[1], 5))
b0, l = bit.tobit(struct.unpack("I4", blob))
b1, l = bit.tobit(struct.unpack("I4", blob, 5))
print("Cmp result", comp_int64s(a0, a1, b0, b1))
EDIT: Added code
I came up with a method that looks like it's working. It's a little ugly though.
The first step is to compare top 32 bits as 2 compliment #’s
MSB sign bit stays, so numbers keep correct relations
-1 —> -1
0 —> 0
9223372036854775807 = 0x7fff ffff ffff ffff -> 0x7ffff ffff = 2147483647
So returning the result from the MSB's works unless they are equal, then the LSB's need to get checked.
I have a few cases to establish the some patterns:
-1 = 0xffff ffff ffff ffff
-2 = 0xffff ffff ffff fffe
32 bit is:
-1 -> 0xffff ffff = -1
-2 -> 0xffff fffe = -2
-1 > -2 would be like -1 > -2 : GOOD
And
8589934591 = 0x0000 0001 ffff ffff
8589934590 = 0x0000 0001 ffff fffe
32 bit is:
8589934591 -> ffff ffff = -1
8589934590 -> ffff fffe = -2
8589934591 > 8589934590 would be -1 > -2 : GOOD
The sign bit on MSB’s doesn’t matter b/c negative numbers have the same relationship between themselves as positive numbers. e.g regardless of sign bit, lsb values of 0xff > 0xfe, always.
What about if the MSB on the lower 32 bits is different?
0xff7f ffff 7fff ffff = -36,028,799,166,447,617
0xff7f ffff ffff ffff = -36,028,797,018,963,969
32 bit is:
-..799.. -> 0x7fff ffff = 2147483647
-..797.. -> 0xffff ffff = -1
-..799.. < -..797.. would be 2147483647 < -1 : BAD!
So we need to ignore the sign bit on the lower 32 bits. And since the relationships are the same for the LSBs regardless of sign, just using
the lowest 32 bits unsigned works for all cases.
This means I want signed for the MSB's and unsigned for the LSBs - so chaging I4 to i4 for the LSBs. Also making big endian official and using '>' on the struct.unpack calls:
-- ...
local comp_int64s = function (as0, au1, bs0, bu1)
if as0 > bs0 then
return 1
elseif as0 < bs0 then
return -1
else
-- msb's equal comparing lsbs - these are unsigned
if au1 > bu1 then
return 1
elseif au1 < bu1 then
return -1
else
return 0
end
end
end
local l, as0, au1, bs0, bu1
as0, l = bit.tobit(struct.unpack(">i4", ARGV[1]))
au1, l = bit.tobit(struct.unpack(">I4", ARGV[1], 5))
bs0, l = bit.tobit(struct.unpack(">i4", blob))
bu1, l = bit.tobit(struct.unpack(">I4", blob, 5))
print("Cmp result", comp_int64s(as0, au1, bs0, bu1))
Comparing is a simple string compare s1 == s2.
Greater than is when not s1 == s2 and i1 < i2.
Less than is the real work. string.byte allows to get single bytes as unsigned char. In case of unsigned integer, you would just have to check bytes-downwards: b1==b2 -> check next byte; through all bytes -> false (equal); b1>b2 -> false (greater than); b1<b2 -> true. Signed requires more steps: first check the sign bit (uppermost byte >127). If sign 1 is set but not sign 2, integer 1 is negative but not integer 2 -> true. The opposite would obviously result in false. When both signs are equal, you can do the unsigned processing.
When you can pack more bytes to an integer, it's fine too, but you have to adjust the sign bit check. When you have LuaJIT, you can use the ffi library to cast your string into a byte array into an int64.
I have a specific requirement to convert a stream of bytes into a character encoding that happens to be 6-bits per character.
Here's an example:
Input: 0x50 0x11 0xa0
Character Table:
010100 T
000001 A
000110 F
100000 SPACE
Output: "TAF "
Logically I can understand how this works:
Taking 0x50 0x11 0xa0 and showing as binary:
01010000 00010001 10100000
Which is "TAF ".
What's the best way to do this programmatically (pseudo code or c++). Thank you!
Well, every 3 bytes, you end up with four characters. So for one thing, you need to work out what to do if the input isn't a multiple of three bytes. (Does it have padding of some kind, like base64?)
Then I'd probably take each 3 bytes in turn. In C#, which is close enough to pseudo-code for C :)
for (int i = 0; i < array.Length; i += 3)
{
// Top 6 bits of byte i
int value1 = array[i] >> 2;
// Bottom 2 bits of byte i, top 4 bits of byte i+1
int value2 = ((array[i] & 0x3) << 4) | (array[i + 1] >> 4);
// Bottom 4 bits of byte i+1, top 2 bits of byte i+2
int value3 = ((array[i + 1] & 0xf) << 2) | (array[i + 2] >> 6);
// Bottom 6 bits of byte i+2
int value4 = array[i + 2] & 0x3f;
// Now use value1...value4, e.g. putting them into a char array.
// You'll need to decode from the 6-bit number (0-63) to the character.
}
Just in case if someone is interested - another variant that extracts 6-bit numbers from the stream as soon as they appear there. That is, results can be obtained even if less then 3 bytes are currently read. Would be useful for unpadded streams.
The code saves the state of the accumulator a in variable n which stores the number of bits left in accumulator from the previous read.
int n = 0;
unsigned char a = 0;
unsigned char b = 0;
while (read_byte(&byte)) {
// save (6-n) most significant bits of input byte to proper position
// in accumulator
a |= (b >> (n + 2)) & (077 >> n);
store_6bit(a);
a = 0;
// save remaining least significant bits of input byte to proper
// position in accumulator
a |= (b << (4 - n)) & ((077 << (4 - n)) & 077);
if (n == 4) {
store_6bit(a);
a = 0;
}
n = (n + 2) % 6;
}