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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
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