[PATCH 12/16] DRBD: variable_length_integer_encoding

[Philipp Reisner <philipp.reisner@linbit.com>]

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Encoding of our simple LRE compression scheme. It is very effective since
large parts of our bitmap are sparse.

Signed-off-by: Philipp Reisner <philipp.reisner@linbit.com>
Signed-off-by: Lars Ellenberg <lars.ellenberg@linbit.com>

---
diff --git a/drivers/block/drbd/drbd_vli.h b/drivers/block/drbd/drbd_vli.h
new file mode 100644
index 0000000..fc82400
--- /dev/null
+++ b/drivers/block/drbd/drbd_vli.h
@@ -0,0 +1,351 @@
+/*
+-*- linux-c -*-
+   drbd_receiver.c
+   This file is part of DRBD by Philipp Reisner and Lars Ellenberg.
+
+   Copyright (C) 2001-2008, LINBIT Information Technologies GmbH.
+   Copyright (C) 1999-2008, Philipp Reisner <philipp.reisner@linbit.com>.
+   Copyright (C) 2002-2008, Lars Ellenberg <lars.ellenberg@linbit.com>.
+
+   drbd is free software; you can redistribute it and/or modify
+   it under the terms of the GNU General Public License as published by
+   the Free Software Foundation; either version 2, or (at your option)
+   any later version.
+
+   drbd is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+   GNU General Public License for more details.
+
+   You should have received a copy of the GNU General Public License
+   along with drbd; see the file COPYING.  If not, write to
+   the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
+ */
+
+#ifndef _DRBD_VLI_H
+#define _DRBD_VLI_H
+
+/*
+ * At a granularity of 4KiB storage represented per bit,
+ * and stroage sizes of several TiB,
+ * and possibly small-bandwidth replication,
+ * the bitmap transfer time can take much too long,
+ * if transmitted in plain text.
+ *
+ * We try to reduce the transfered bitmap information
+ * by encoding runlengths of bit polarity.
+ *
+ * We never actually need to encode a "zero" (runlengths are positive).
+ * But then we have to store the value of the first bit.
+ * The first bit of information thus shall encode if the first runlength
+ * gives the number of set or unset bits.
+ *
+ * We assume that large areas are either completely set or unset,
+ * which gives good compression with any runlength method,
+ * even when encoding the runlength as fixed size 32bit/64bit integers.
+ *
+ * Still, there may be areas where the polarity flips every few bits,
+ * and encoding the runlength sequence of those areas with fix size
+ * integers would be much worse than plaintext.
+ *
+ * We want to encode small runlength values with minimum code length,
+ * while still being able to encode a Huge run of all zeros.
+ *
+ * Thus we need a Variable Length Integer encoding, VLI.
+ *
+ * For some cases, we produce more code bits than plaintext input.
+ * We need to send incompressible chunks as plaintext, skip over them
+ * and then see if the next chunk compresses better.
+ *
+ * We don't care too much about "excellent" compression ratio for large
+ * runlengths (all set/all clear): whether we achieve a factor of 100
+ * or 1000 is not that much of an issue.
+ * We do not want to waste too much on short runlengths in the "noisy"
+ * parts of the bitmap, though.
+ *
+ * There are endless variants of VLI, we experimented with:
+ *  * simple byte-based
+ *  * various bit based with different code word length.
+ *
+ * To avoid yet an other configuration parameter (choice of bitmap compression
+ * algorithm) which was difficult to explain and tune, we just chose the one
+ * variant that turned out best in all test cases.
+ * Based on real world usage patterns, with device sizes ranging from a few GiB
+ * to several TiB, file server/mailserver/webserver/mysql/postgress,
+ * mostly idle to really busy, the all time winner (though sometimes only
+ * marginally better) is:
+ */
+
+/*
+ * encoding is "visualised" as
+ * __little endian__ bitstream, least significant bit first (left most)
+ *
+ * this particular encoding is chosen so that the prefix code
+ * starts as unary encoding the level, then modified so that
+ * 10 levels can be described in 8bit, with minimal overhead
+ * for the smaller levels.
+ *
+ * Number of data bits follow fibonacci sequence, with the exception of the
+ * last level (+1 data bit, so it makes 64bit total).  The only worse code when
+ * encoding bit polarity runlength is 1 plain bits => 2 code bits.
+prefix    data bits                                    max val  Nº data bits
+0 x                                                         0x2            1
+10 x                                                        0x4            1
+110 xx                                                      0x8            2
+1110 xxx                                                   0x10            3
+11110 xxx xx                                               0x30            5
+111110 xx xxxxxx                                          0x130            8
+11111100  xxxxxxxx xxxxx                                 0x2130           13
+11111110  xxxxxxxx xxxxxxxx xxxxx                      0x202130           21
+11111101  xxxxxxxx xxxxxxxx xxxxxxxx  xxxxxxxx xx   0x400202130           34
+11111111  xxxxxxxx xxxxxxxx xxxxxxxx  xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx 56
+ * maximum encodable value: 0x100000400202130 == 2**56 + some */
+
+/* compression "table":
+ transmitted   x                                0.29
+ as plaintext x                                  ........................
+             x                                   ........................
+            x                                    ........................
+           x    0.59                         0.21........................
+          x      ........................................................
+         x       .. c ...................................................
+        x    0.44.. o ...................................................
+       x .......... d ...................................................
+      x  .......... e ...................................................
+     X.............   ...................................................
+    x.............. b ...................................................
+2.0x............... i ...................................................
+ #X................ t ...................................................
+ #................. s ...........................  plain bits  ..........
+-+-----------------------------------------------------------------------
+ 1             16              32                              64
+*/
+
+/* LEVEL: (total bits, prefix bits, prefix value),
+ * sorted ascending by number of total bits.
+ * The rest of the code table is calculated at compiletime from this. */
+
+/* fibonacci data 1, 1, ... */
+#define VLI_L_1_1() do { \
+	LEVEL( 2, 1, 0x00); \
+	LEVEL( 3, 2, 0x01); \
+	LEVEL( 5, 3, 0x03); \
+	LEVEL( 7, 4, 0x07); \
+	LEVEL(10, 5, 0x0f); \
+	LEVEL(14, 6, 0x1f); \
+	LEVEL(21, 8, 0x3f); \
+	LEVEL(29, 8, 0x7f); \
+	LEVEL(42, 8, 0xbf); \
+	LEVEL(64, 8, 0xff); \
+	} while (0)
+
+/* finds a suitable level to decode the least significant part of in.
+ * returns number of bits consumed.
+ *
+ * BUG() for bad input, as that would mean a buggy code table. */
+static inline int vli_decode_bits(u64 *out, const u64 in)
+{
+	u64 adj = 1;
+
+#define LEVEL(t,b,v)					\
+	do {						\
+		if ((in & ((1 << b) -1)) == v) {	\
+			*out = ((in & ((~0ULL) >> (64-t))) >> b) + adj;	\
+			return t;			\
+		}					\
+		adj += 1ULL << (t - b);			\
+	} while (0)
+
+	VLI_L_1_1();
+
+	/* NOT REACHED, if VLI_LEVELS code table is defined properly */
+	BUG();
+#undef LEVEL
+}
+
+/* return number of code bits needed,
+ * or negative error number */
+static inline int __vli_encode_bits(u64 *out, const u64 in)
+{
+	u64 max = 0;
+	u64 adj = 1;
+
+	if (in == 0)
+		return -EINVAL;
+
+#define LEVEL(t,b,v) do {		\
+		max += 1ULL << (t - b);	\
+		if (in <= max) {	\
+			if (out)	\
+				*out = ((in - adj) << b) | v;	\
+			return t;	\
+		}			\
+		adj = max + 1;		\
+	} while (0)
+
+	VLI_L_1_1();
+
+	return -EOVERFLOW;
+#undef LEVEL
+}
+
+#undef VLI_L_1_1
+
+/* code from here down is independend of actually used bit code */
+
+/*
+ * Code length is determined by some unique (e.g. unary) prefix.
+ * This encodes arbitrary bit length, not whole bytes: we have a bit-stream,
+ * not a byte stream.
+ */
+
+/* for the bitstream, we need a cursor */
+struct bitstream_cursor {
+	/* the current byte */
+	u8 *b;
+	/* the current bit within *b, nomalized: 0..7 */
+	unsigned int bit;
+};
+
+/* initialize cursor to point to first bit of stream */
+static inline void bitstream_cursor_reset(struct bitstream_cursor *cur, void *s)
+{
+	cur->b = s;
+	cur->bit = 0;
+}
+
+/* advance cursor by that many bits; maximum expected input value: 64,
+ * but depending on VLI implementation, it may be more. */
+static inline void bitstream_cursor_advance(struct bitstream_cursor *cur, unsigned int bits)
+{
+	bits += cur->bit;
+	cur->b = cur->b + (bits >> 3);
+	cur->bit = bits & 7;
+}
+
+/* the bitstream itself knows its length */
+struct bitstream {
+	struct bitstream_cursor cur;
+	unsigned char *buf;
+	size_t buf_len;		/* in bytes */
+
+	/* for input stream:
+	 * number of trailing 0 bits for padding
+	 * total number of valid bits in stream: buf_len * 8 - pad_bits */
+	unsigned int pad_bits;
+};
+
+static inline void bitstream_init(struct bitstream *bs, void *s, size_t len, unsigned int pad_bits)
+{
+	bs->buf = s;
+	bs->buf_len = len;
+	bs->pad_bits = pad_bits;
+	bitstream_cursor_reset(&bs->cur, bs->buf);
+}
+
+static inline void bitstream_rewind(struct bitstream *bs)
+{
+	bitstream_cursor_reset(&bs->cur, bs->buf);
+	memset(bs->buf, 0, bs->buf_len);
+}
+
+/* Put (at most 64) least significant bits of val into bitstream, and advance cursor.
+ * Ignores "pad_bits".
+ * Returns zero if bits == 0 (nothing to do).
+ * Returns number of bits used if successful.
+ *
+ * If there is not enough room left in bitstream,
+ * leaves bitstream unchanged and returns -ENOBUFS.
+ */
+static inline int bitstream_put_bits(struct bitstream *bs, u64 val, const unsigned int bits)
+{
+	unsigned char *b = bs->cur.b;
+	unsigned int tmp;
+
+	if (bits == 0)
+		return 0;
+
+	if ((bs->cur.b + ((bs->cur.bit + bits -1) >> 3)) - bs->buf >= bs->buf_len)
+		return -ENOBUFS;
+
+	/* paranoia: strip off hi bits; they should not be set anyways. */
+	if (bits < 64)
+		val &= ~0ULL >> (64 - bits);
+
+	*b++ |= (val & 0xff) << bs->cur.bit;
+
+	for (tmp = 8 - bs->cur.bit; tmp < bits; tmp += 8)
+		*b++ |= (val >> tmp) & 0xff;
+
+	bitstream_cursor_advance(&bs->cur, bits);
+	return bits;
+}
+
+/* Fetch (at most 64) bits from bitstream into *out, and advance cursor.
+ *
+ * If more than 64 bits are requested, returns -EINVAL and leave *out unchanged.
+ *
+ * If there are less than the requested number of valid bits left in the
+ * bitstream, still fetches all available bits.
+ *
+ * Returns number of actually fetched bits.
+ */
+static inline int bitstream_get_bits(struct bitstream *bs, u64 *out, int bits)
+{
+	u64 val;
+	unsigned int n;
+
+	if (bits > 64)
+		return -EINVAL;
+
+	if (bs->cur.b + ((bs->cur.bit + bs->pad_bits + bits -1) >> 3) - bs->buf >= bs->buf_len)
+		bits = ((bs->buf_len - (bs->cur.b - bs->buf)) << 3)
+			- bs->cur.bit - bs->pad_bits;
+
+	if (bits == 0) {
+		*out = 0;
+		return 0;
+	}
+
+	/* get the high bits */
+	val = 0;
+	n = (bs->cur.bit + bits + 7) >> 3;
+	/* n may be at most 9, if cur.bit + bits > 64 */
+	/* which means this copies at most 8 byte */
+	if (n) {
+		memcpy(&val, bs->cur.b+1, n - 1);
+		val = le64_to_cpu(val) << (8 - bs->cur.bit);
+	}
+
+	/* we still need the low bits */
+	val |= bs->cur.b[0] >> bs->cur.bit;
+
+	/* and mask out bits we don't want */
+	val &= ~0ULL >> (64 - bits);
+
+	bitstream_cursor_advance(&bs->cur, bits);
+	*out = val;
+
+	return bits;
+}
+
+/* encodes @in as vli into @bs;
+
+ * return values
+ *  > 0: number of bits successfully stored in bitstream
+ * -ENOBUFS @bs is full
+ * -EINVAL input zero (invalid)
+ * -EOVERFLOW input too large for this vli code (invalid)
+ */
+static inline int vli_encode_bits(struct bitstream *bs, u64 in)
+{
+	u64 code = code;
+	int bits = __vli_encode_bits(&code, in);
+
+	if (bits <= 0)
+		return bits;
+
+	return bitstream_put_bits(bs, code, bits);
+}
+
+#endif