How to reverse bits of a byte?

Question

For example, in PHP, how would I reverse the bits of the byte 11011111 to 11111011?

Solution 1

If you have already the bits in the form of a string, use strrev.

If not, convert first the byte to its binary representation by using decbin, then reverse using strrev, then go back to byte (if necessary) by using bindec.

Solution 2

The straight forward approach is to perform 8 masks, 8 rotates, and 7 additions:

$blah = $blah & 128 >> 7 + $blah & 64 >> 5 + $blah & 32 >> 3 + $blah & 16 >> 1 + $blah & 8 << 1 + $blah & 4 << 3 + $blah & 2 << 5 + $blah & 1 << 7;

Solution 3

Check the section on reversing bit sequences in Bit Twiddling Hacks. Should be easy to adapt one of the techniques into PHP.

While probably not practical for PHP, there's a particularly fascinating one using 3 64bit operations:

unsigned char b; // reverse this (8-bit) byte
b = (b * 0x0202020202ULL & 0x010884422010ULL) % 1023;

Solution 4

The quickest way, but also the one requiring more space is a lookup, whereby each possible value of a byte (256 if you go for the whole range), is associated with its "reversed" equivalent.

If you only have a few such bytes to handle, bit-wise operators will do but that will be slower, maybe something like:

function reverseBits($in) {
  $out = 0;

  if ($in & 0x01) $out |= 0x80;
  if ($in & 0x02) $out |= 0x40;
  if ($in & 0x04) $out |= 0x20;
  if ($in & 0x08) $out |= 0x10;
  if ($in & 0x10) $out |= 0x08;
  if ($in & 0x20) $out |= 0x04;
  if ($in & 0x40) $out |= 0x02;
  if ($in & 0x80) $out |= 0x01;

  return $out;
}

Solution 5

Some people have been suggesting a lookup table, while I have been making one:

[
        0x00, 0x80, 0x40, 0xC0, 0x20, 0xA0, 0x60, 0xE0, 0x10, 0x90, 0x50, 0xD0, 0x30, 0xB0, 0x70, 0xF0,
        0x08, 0x88, 0x48, 0xC8, 0x28, 0xA8, 0x68, 0xE8, 0x18, 0x98, 0x58, 0xD8, 0x38, 0xB8, 0x78, 0xF8,
        0x04, 0x84, 0x44, 0xC4, 0x24, 0xA4, 0x64, 0xE4, 0x14, 0x94, 0x54, 0xD4, 0x34, 0xB4, 0x74, 0xF4,
        0x0C, 0x8C, 0x4C, 0xCC, 0x2C, 0xAC, 0x6C, 0xEC, 0x1C, 0x9C, 0x5C, 0xDC, 0x3C, 0xBC, 0x7C, 0xFC,
        0x02, 0x82, 0x42, 0xC2, 0x22, 0xA2, 0x62, 0xE2, 0x12, 0x92, 0x52, 0xD2, 0x32, 0xB2, 0x72, 0xF2,
        0x0A, 0x8A, 0x4A, 0xCA, 0x2A, 0xAA, 0x6A, 0xEA, 0x1A, 0x9A, 0x5A, 0xDA, 0x3A, 0xBA, 0x7A, 0xFA,
        0x06, 0x86, 0x46, 0xC6, 0x26, 0xA6, 0x66, 0xE6, 0x16, 0x96, 0x56, 0xD6, 0x36, 0xB6, 0x76, 0xF6,
        0x0E, 0x8E, 0x4E, 0xCE, 0x2E, 0xAE, 0x6E, 0xEE, 0x1E, 0x9E, 0x5E, 0xDE, 0x3E, 0xBE, 0x7E, 0xFE,
        0x01, 0x81, 0x41, 0xC1, 0x21, 0xA1, 0x61, 0xE1, 0x11, 0x91, 0x51, 0xD1, 0x31, 0xB1, 0x71, 0xF1,
        0x09, 0x89, 0x49, 0xC9, 0x29, 0xA9, 0x69, 0xE9, 0x19, 0x99, 0x59, 0xD9, 0x39, 0xB9, 0x79, 0xF9,
        0x05, 0x85, 0x45, 0xC5, 0x25, 0xA5, 0x65, 0xE5, 0x15, 0x95, 0x55, 0xD5, 0x35, 0xB5, 0x75, 0xF5,
        0x0D, 0x8D, 0x4D, 0xCD, 0x2D, 0xAD, 0x6D, 0xED, 0x1D, 0x9D, 0x5D, 0xDD, 0x3D, 0xBD, 0x7D, 0xFD,
        0x03, 0x83, 0x43, 0xC3, 0x23, 0xA3, 0x63, 0xE3, 0x13, 0x93, 0x53, 0xD3, 0x33, 0xB3, 0x73, 0xF3,
        0x0B, 0x8B, 0x4B, 0xCB, 0x2B, 0xAB, 0x6B, 0xEB, 0x1B, 0x9B, 0x5B, 0xDB, 0x3B, 0xBB, 0x7B, 0xFB,
        0x07, 0x87, 0x47, 0xC7, 0x27, 0xA7, 0x67, 0xE7, 0x17, 0x97, 0x57, 0xD7, 0x37, 0xB7, 0x77, 0xF7,
        0x0F, 0x8F, 0x4F, 0xCF, 0x2F, 0xAF, 0x6F, 0xEF, 0x1F, 0x9F, 0x5F, 0xDF, 0x3F, 0xBF, 0x7F, 0xFF,
][$byte]

And here's a character version:

[
    "\x00", "\x80", "\x40", "\xC0", "\x20", "\xA0", "\x60", "\xE0", "\x10", "\x90", "\x50", "\xD0", "\x30", "\xB0", "\x70", "\xF0",
    "\x08", "\x88", "\x48", "\xC8", "\x28", "\xA8", "\x68", "\xE8", "\x18", "\x98", "\x58", "\xD8", "\x38", "\xB8", "\x78", "\xF8",
    "\x04", "\x84", "\x44", "\xC4", "\x24", "\xA4", "\x64", "\xE4", "\x14", "\x94", "\x54", "\xD4", "\x34", "\xB4", "\x74", "\xF4",
    "\x0C", "\x8C", "\x4C", "\xCC", "\x2C", "\xAC", "\x6C", "\xEC", "\x1C", "\x9C", "\x5C", "\xDC", "\x3C", "\xBC", "\x7C", "\xFC",
    "\x02", "\x82", "\x42", "\xC2", "\x22", "\xA2", "\x62", "\xE2", "\x12", "\x92", "\x52", "\xD2", "\x32", "\xB2", "\x72", "\xF2",
    "\x0A", "\x8A", "\x4A", "\xCA", "\x2A", "\xAA", "\x6A", "\xEA", "\x1A", "\x9A", "\x5A", "\xDA", "\x3A", "\xBA", "\x7A", "\xFA",
    "\x06", "\x86", "\x46", "\xC6", "\x26", "\xA6", "\x66", "\xE6", "\x16", "\x96", "\x56", "\xD6", "\x36", "\xB6", "\x76", "\xF6",
    "\x0E", "\x8E", "\x4E", "\xCE", "\x2E", "\xAE", "\x6E", "\xEE", "\x1E", "\x9E", "\x5E", "\xDE", "\x3E", "\xBE", "\x7E", "\xFE",
    "\x01", "\x81", "\x41", "\xC1", "\x21", "\xA1", "\x61", "\xE1", "\x11", "\x91", "\x51", "\xD1", "\x31", "\xB1", "\x71", "\xF1",
    "\x09", "\x89", "\x49", "\xC9", "\x29", "\xA9", "\x69", "\xE9", "\x19", "\x99", "\x59", "\xD9", "\x39", "\xB9", "\x79", "\xF9",
    "\x05", "\x85", "\x45", "\xC5", "\x25", "\xA5", "\x65", "\xE5", "\x15", "\x95", "\x55", "\xD5", "\x35", "\xB5", "\x75", "\xF5",
    "\x0D", "\x8D", "\x4D", "\xCD", "\x2D", "\xAD", "\x6D", "\xED", "\x1D", "\x9D", "\x5D", "\xDD", "\x3D", "\xBD", "\x7D", "\xFD",
    "\x03", "\x83", "\x43", "\xC3", "\x23", "\xA3", "\x63", "\xE3", "\x13", "\x93", "\x53", "\xD3", "\x33", "\xB3", "\x73", "\xF3",
    "\x0B", "\x8B", "\x4B", "\xCB", "\x2B", "\xAB", "\x6B", "\xEB", "\x1B", "\x9B", "\x5B", "\xDB", "\x3B", "\xBB", "\x7B", "\xFB",
    "\x07", "\x87", "\x47", "\xC7", "\x27", "\xA7", "\x67", "\xE7", "\x17", "\x97", "\x57", "\xD7", "\x37", "\xB7", "\x77", "\xF7",
    "\x0F", "\x8F", "\x4F", "\xCF", "\x2F", "\xAF", "\x6F", "\xEF", "\x1F", "\x9F", "\x5F", "\xDF", "\x3F", "\xBF", "\x7F", "\xFF",
][ord($byte)];

View more solutions

Comments

[tmsppc]

@Kinopiko: 3 upvotes, with mine. Do you have a better solution. Post it and you'll get my vote too!

[Arthur Reutenauer]

Well, it is answering the question :-)

[Lukman]

The best answer IMO that will work for general cases. Those bit shifting, rotation etc are just targeting the example value given and won't work for random binary strings ..

[Lukman]

which mathematical theorem or algorithm is this answer based on?

[Pramod Prajapati]

+1 This is what I would have suggested had I not botched the initial understanding.

[skirmish]

Historically, I've found that having a 256 byte lookup table is the fastest way to achieve it as it's just a lookup. 256 bytes is not a lot of space to dedicate to something like this if it need to be fast. Though the above reverseBits function is about as small and tight as you can get the code without having a lookup. Also for one small optimization you could change the first { $out |= 0x80;} to { $out = 0x80;} as you know that first time you're ORing with 0.

[mjv]

@skirmish, agreed, I'd tend to use the lookup array in most cases. An intermediate solution, would be to have a smaller array, for 4 bits, and do two lookups with the associated multiplication/division for the leftmost bit-quad). This way of doing can also be used to deal with say integers rather that bytes. (The downside of the lookup approach is that its space requirement grows exponentially, whereby the coded appraoch linearly (w/ regards to the number of bits).

[kliron]

if you're performing the operation just once, a lookup table is bad. But if it's a frequent operation, it should outperform any other approach.

[Mask]

Can you explain what "ULL" means here?

[PeterAllenWebb]

@mask that's an unsigned long long, the suffix tells the compiler that what proceeds it is a 64-bit unsigned integer literal.

[Epsilon Prime]

"The Principle of Brute Force"

[denoise]

why it's a solution if it is not practical for php?

[bryc]

It's not a theorem, its literally just reconstructing a byte by rearranging the bits. I had to use parenthesis and OR instead of + though: (128&n)>>7|(64&n)>>5|(32&n)>>3|(16&n)>>1|(8&n)<<1|(4&n)<<3|(‌​2&n)<<5|(1&n)<<7