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77c89e0 Feb 18, 2014
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// Simple byte-aligned rANS encoder/decoder - public domain - Fabian 'ryg' Giesen 2014
//
// Not intended to be "industrial strength"; just meant to illustrate the general
// idea.
#ifndef RANS_BYTE_HEADER
#define RANS_BYTE_HEADER
#include <stdint.h>
#ifdef assert
#define RansAssert assert
#else
#define RansAssert(x)
#endif
// READ ME FIRST:
//
// This is designed like a typical arithmetic coder API, but there's three
// twists you absolutely should be aware of before you start hacking:
//
// 1. You need to encode data in *reverse* - last symbol first. rANS works
// like a stack: last in, first out.
// 2. Likewise, the encoder outputs bytes *in reverse* - that is, you give
// it a pointer to the *end* of your buffer (exclusive), and it will
// slowly move towards the beginning as more bytes are emitted.
// 3. Unlike basically any other entropy coder implementation you might
// have used, you can interleave data from multiple independent rANS
// encoders into the same bytestream without any extra signaling;
// you can also just write some bytes by yourself in the middle if
// you want to. This is in addition to the usual arithmetic encoder
// property of being able to switch models on the fly. Writing raw
// bytes can be useful when you have some data that you know is
// incompressible, and is cheaper than going through the rANS encode
// function. Using multiple rANS coders on the same byte stream wastes
// a few bytes compared to using just one, but execution of two
// independent encoders can happen in parallel on superscalar and
// Out-of-Order CPUs, so this can be *much* faster in tight decoding
// loops.
//
// This is why all the rANS functions take the write pointer as an
// argument instead of just storing it in some context struct.
// --------------------------------------------------------------------------
// L ('l' in the paper) is the lower bound of our normalization interval.
// Between this and our byte-aligned emission, we use 31 (not 32!) bits.
// This is done intentionally because exact reciprocals for 31-bit uints
// fit in 32-bit uints: this permits some optimizations during encoding.
#define RANS_BYTE_L (1u << 23) // lower bound of our normalization interval
// State for a rANS encoder. Yep, that's all there is to it.
typedef uint32_t RansState;
// Initialize a rANS encoder.
static inline void RansEncInit(RansState* r)
{
*r = RANS_BYTE_L;
}
// Renormalize the encoder. Internal function.
static inline RansState RansEncRenorm(RansState x, uint8_t** pptr, uint32_t freq, uint32_t scale_bits)
{
uint32_t x_max = ((RANS_BYTE_L >> scale_bits) << 8) * freq; // this turns into a shift.
if (x >= x_max) {
uint8_t* ptr = *pptr;
do {
*--ptr = (uint8_t) (x & 0xff);
x >>= 8;
} while (x >= x_max);
*pptr = ptr;
}
return x;
}
// Encodes a single symbol with range start "start" and frequency "freq".
// All frequencies are assumed to sum to "1 << scale_bits", and the
// resulting bytes get written to ptr (which is updated).
//
// NOTE: With rANS, you need to encode symbols in *reverse order*, i.e. from
// beginning to end! Likewise, the output bytestream is written *backwards*:
// ptr starts pointing at the end of the output buffer and keeps decrementing.
static inline void RansEncPut(RansState* r, uint8_t** pptr, uint32_t start, uint32_t freq, uint32_t scale_bits)
{
// renormalize
RansState x = RansEncRenorm(*r, pptr, freq, scale_bits);
// x = C(s,x)
*r = ((x / freq) << scale_bits) + (x % freq) + start;
}
// Flushes the rANS encoder.
static inline void RansEncFlush(RansState* r, uint8_t** pptr)
{
uint32_t x = *r;
uint8_t* ptr = *pptr;
ptr -= 4;
ptr[0] = (uint8_t) (x >> 0);
ptr[1] = (uint8_t) (x >> 8);
ptr[2] = (uint8_t) (x >> 16);
ptr[3] = (uint8_t) (x >> 24);
*pptr = ptr;
}
// Initializes a rANS decoder.
// Unlike the encoder, the decoder works forwards as you'd expect.
static inline void RansDecInit(RansState* r, uint8_t** pptr)
{
uint32_t x;
uint8_t* ptr = *pptr;
x = ptr[0] << 0;
x |= ptr[1] << 8;
x |= ptr[2] << 16;
x |= ptr[3] << 24;
ptr += 4;
*pptr = ptr;
*r = x;
}
// Returns the current cumulative frequency (map it to a symbol yourself!)
static inline uint32_t RansDecGet(RansState* r, uint32_t scale_bits)
{
return *r & ((1u << scale_bits) - 1);
}
// Advances in the bit stream by "popping" a single symbol with range start
// "start" and frequency "freq". All frequencies are assumed to sum to "1 << scale_bits",
// and the resulting bytes get written to ptr (which is updated).
static inline void RansDecAdvance(RansState* r, uint8_t** pptr, uint32_t start, uint32_t freq, uint32_t scale_bits)
{
uint32_t mask = (1u << scale_bits) - 1;
// s, x = D(x)
uint32_t x = *r;
x = freq * (x >> scale_bits) + (x & mask) - start;
// renormalize
if (x < RANS_BYTE_L) {
uint8_t* ptr = *pptr;
do x = (x << 8) | *ptr++; while (x < RANS_BYTE_L);
*pptr = ptr;
}
*r = x;
}
// --------------------------------------------------------------------------
// That's all you need for a full encoder; below here are some utility
// functions with extra convenience or optimizations.
// Encoder symbol description
// This (admittedly odd) selection of parameters was chosen to make
// RansEncPutSymbol as cheap as possible.
typedef struct {
uint32_t x_max; // (Exclusive) upper bound of pre-normalization interval
uint32_t rcp_freq; // Fixed-point reciprocal frequency
uint32_t bias; // Bias
uint16_t cmpl_freq; // Complement of frequency: (1 << scale_bits) - freq
uint16_t rcp_shift; // Reciprocal shift
} RansEncSymbol;
// Decoder symbols are straightforward.
typedef struct {
uint16_t start; // Start of range.
uint16_t freq; // Symbol frequency.
} RansDecSymbol;
// Initializes an encoder symbol to start "start" and frequency "freq"
static inline void RansEncSymbolInit(RansEncSymbol* s, uint32_t start, uint32_t freq, uint32_t scale_bits)
{
RansAssert(scale_bits <= 16);
RansAssert(start <= (1u << scale_bits));
RansAssert(freq <= (1u << scale_bits) - start);
// Say M := 1 << scale_bits.
//
// The original encoder does:
// x_new = (x/freq)*M + start + (x%freq)
//
// The fast encoder does (schematically):
// q = mul_hi(x, rcp_freq) >> rcp_shift (division)
// r = x - q*freq (remainder)
// x_new = q*M + bias + r (new x)
// plugging in r into x_new yields:
// x_new = bias + x + q*(M - freq)
// =: bias + x + q*cmpl_freq (*)
//
// and we can just precompute cmpl_freq. Now we just need to
// set up our parameters such that the original encoder and
// the fast encoder agree.
s->x_max = ((RANS_BYTE_L >> scale_bits) << 8) * freq;
s->cmpl_freq = (uint16_t) ((1 << scale_bits) - freq);
if (freq < 2) {
// freq=0 symbols are never valid to encode, so it doesn't matter what
// we set our values to.
//
// freq=1 is tricky, since the reciprocal of 1 is 1; unfortunately,
// our fixed-point reciprocal approximation can only multiply by values
// smaller than 1.
//
// So we use the "next best thing": rcp_freq=0xffffffff, rcp_shift=0.
// This gives:
// q = mul_hi(x, rcp_freq) >> rcp_shift
// = mul_hi(x, (1<<32) - 1)) >> 0
// = floor(x - x/(2^32))
// = x - 1 if 1 <= x < 2^32
// and we know that x>0 (x=0 is never in a valid normalization interval).
//
// So we now need to choose the other parameters such that
// x_new = x*M + start
// plug it in:
// x*M + start (desired result)
// = bias + x + q*cmpl_freq (*)
// = bias + x + (x - 1)*(M - 1) (plug in q=x-1, cmpl_freq)
// = bias + 1 + (x - 1)*M
// = x*M + (bias + 1 - M)
//
// so we have start = bias + 1 - M, or equivalently
// bias = start + M - 1.
s->rcp_freq = ~0u;
s->rcp_shift = 0;
s->bias = start + (1 << scale_bits) - 1;
} else {
// Alverson, "Integer Division using reciprocals"
// shift=ceil(log2(freq))
uint32_t shift = 0;
while (freq > (1u << shift))
shift++;
s->rcp_freq = (uint32_t) (((1ull << (shift + 31)) + freq-1) / freq);
s->rcp_shift = shift - 1;
// With these values, 'q' is the correct quotient, so we
// have bias=start.
s->bias = start;
}
}
// Initialize a decoder symbol to start "start" and frequency "freq"
static inline void RansDecSymbolInit(RansDecSymbol* s, uint32_t start, uint32_t freq)
{
RansAssert(start <= (1 << 16));
RansAssert(freq <= (1 << 16) - start);
s->start = (uint16_t) start;
s->freq = (uint16_t) freq;
}
// Encodes a given symbol. This is faster than straight RansEnc since we can do
// multiplications instead of a divide.
//
// See RansEncSymbolInit for a description of how this works.
static inline void RansEncPutSymbol(RansState* r, uint8_t** pptr, RansEncSymbol const* sym)
{
RansAssert(sym->x_max != 0); // can't encode symbol with freq=0
// renormalize
uint32_t x = *r;
uint32_t x_max = sym->x_max;
if (x >= x_max) {
uint8_t* ptr = *pptr;
do {
*--ptr = (uint8_t) (x & 0xff);
x >>= 8;
} while (x >= x_max);
*pptr = ptr;
}
// x = C(s,x)
// NOTE: written this way so we get a 32-bit "multiply high" when
// available. If you're on a 64-bit platform with cheap multiplies
// (e.g. x64), just bake the +32 into rcp_shift.
uint32_t q = (uint32_t) (((uint64_t)x * sym->rcp_freq) >> 32) >> sym->rcp_shift;
*r = x + sym->bias + q * sym->cmpl_freq;
}
// Equivalent to RansDecAdvance that takes a symbol.
static inline void RansDecAdvanceSymbol(RansState* r, uint8_t** pptr, RansDecSymbol const* sym, uint32_t scale_bits)
{
RansDecAdvance(r, pptr, sym->start, sym->freq, scale_bits);
}
// Advances in the bit stream by "popping" a single symbol with range start
// "start" and frequency "freq". All frequencies are assumed to sum to "1 << scale_bits".
// No renormalization or output happens.
static inline void RansDecAdvanceStep(RansState* r, uint32_t start, uint32_t freq, uint32_t scale_bits)
{
uint32_t mask = (1u << scale_bits) - 1;
// s, x = D(x)
uint32_t x = *r;
*r = freq * (x >> scale_bits) + (x & mask) - start;
}
// Equivalent to RansDecAdvanceStep that takes a symbol.
static inline void RansDecAdvanceSymbolStep(RansState* r, RansDecSymbol const* sym, uint32_t scale_bits)
{
RansDecAdvanceStep(r, sym->start, sym->freq, scale_bits);
}
// Renormalize.
static inline void RansDecRenorm(RansState* r, uint8_t** pptr)
{
// renormalize
uint32_t x = *r;
if (x < RANS_BYTE_L) {
uint8_t* ptr = *pptr;
do x = (x << 8) | *ptr++; while (x < RANS_BYTE_L);
*pptr = ptr;
}
*r = x;
}
#endif // RANS_BYTE_HEADER