linux-kernel - There are smaller ways to encode a CRC32 table...

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Date:	Thu, 31 Jan 2008 23:53:20 -0500
From:	"George Spelvin" <linux@...izon.com>
To:	hpa@...or.com, ijc@...lion.org.uk
Cc:	linux@...izon.com, linux-kernel@...r.kernel.org,
	tglx@...utronix.de, mingo@...hat.com, hpa@...or.com
Subject: There are smaller ways to encode a CRC32 table...

The code to fill it in is smaller than the table itself.
Is it worth complicating things with some INIT code to reduce
the stored image size?  (The table is not compressible.)

#define CRC32POLY	0xedb88320	/* CRC32 polynomial, little-endian */

static uint32_t crctab32[256];

void
crc32init(void)
{
	unsigned i, j;
	uint32_t crc = 1;

	crctab32[0] = 0;

	for (i = 128; i; i >>= 1) {
		crc = (crc >> 1) ^ ((crc & 1) ? CRC32POLY : 0);
		for (j = 0; j < 256; j += 2*i)
			crctab32[i+j] = crc ^ crctab32[j];
	}
}

The above code basically computes the CRCs of the bytes 0x80, 0x40, ... 0x01,
and applies the identity crctab32[i^j] = crctab32[i] ^ crctab32[j].

And BTW, storing the inverse of the CRC only catches trailing (after the CRC)
all-zero padding.  If this is not a problem, it's not necessary, although you
still might want to do it just for consistency.  This inversion changes the
CRC of the entire image (body + CRC) from all-zero to a fixed non-zero value.
(To be precise, to the (non-inverted) CRC of 0xffffffff.)
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