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- // 64-bit rANS encoder/decoder - public domain - Fabian 'ryg' Giesen 2014
- //
- // This uses 64-bit states (63-bit actually) which allows renormalizing
- // by writing out a whole 32 bits at a time (b=2^32) while still
- // retaining good precision and allowing for high probability resolution.
- //
- // The only caveat is that this version requires 64-bit arithmetic; in
- // particular, the encoder approximation in the bottom half requires a
- // fast way to obtain the top 64 bits of an unsigned 64*64 bit product.
- //
- // In short, as written, this code works on 64-bit targets only!
-
- #ifndef RANS64_HEADER
- #define RANS64_HEADER
-
- #include <stdint.h>
-
- #ifdef assert
- #define Rans64Assert assert
- #else
- #define Rans64Assert(x)
- #endif
-
- // --------------------------------------------------------------------------
-
- // This code needs support for 64-bit long multiplies with 128-bit result
- // (or more precisely, the top 64 bits of a 128-bit result). This is not
- // really portable functionality, so we need some compiler-specific hacks
- // here.
-
- #if defined(_MSC_VER)
-
- #include <intrin.h>
-
- static inline uint64_t Rans64MulHi(uint64_t a, uint64_t b)
- {
- return __umulh(a, b);
- }
-
- #elif defined(__GNUC__)
-
- static inline uint64_t Rans64MulHi(uint64_t a, uint64_t b)
- {
- return (uint64_t) (((unsigned __int128)a * b) >> 64);
- }
-
- #else
-
- #error Unknown/unsupported compiler!
-
- #endif
-
- // --------------------------------------------------------------------------
-
- // L ('l' in the paper) is the lower bound of our normalization interval.
- // Between this and our 32-bit-aligned emission, we use 63 (not 64!) bits.
- // This is done intentionally because exact reciprocals for 63-bit uints
- // fit in 64-bit uints: this permits some optimizations during encoding.
- #define RANS64_L (1ull << 31) // lower bound of our normalization interval
-
- // State for a rANS encoder. Yep, that's all there is to it.
- typedef uint64_t Rans64State;
-
- // Initialize a rANS encoder.
- static inline void Rans64EncInit(Rans64State* r)
- {
- *r = RANS64_L;
- }
-
- // 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 Rans64EncPut(Rans64State* r, uint32_t** pptr, uint32_t start, uint32_t freq, uint32_t scale_bits)
- {
- Rans64Assert(freq != 0);
-
- // renormalize (never needs to loop)
- uint64_t x = *r;
- uint64_t x_max = ((RANS64_L >> scale_bits) << 32) * freq; // this turns into a shift.
- if (x >= x_max) {
- *pptr -= 1;
- **pptr = (uint32_t) x;
- x >>= 32;
- Rans64Assert(x < x_max);
- }
-
- // x = C(s,x)
- *r = ((x / freq) << scale_bits) + (x % freq) + start;
- }
-
- // Flushes the rANS encoder.
- static inline void Rans64EncFlush(Rans64State* r, uint32_t** pptr)
- {
- uint64_t x = *r;
-
- *pptr -= 2;
- (*pptr)[0] = (uint32_t) (x >> 0);
- (*pptr)[1] = (uint32_t) (x >> 32);
- }
-
- // Initializes a rANS decoder.
- // Unlike the encoder, the decoder works forwards as you'd expect.
- static inline void Rans64DecInit(Rans64State* r, uint32_t** pptr)
- {
- uint64_t x;
-
- x = (uint64_t) ((*pptr)[0]) << 0;
- x |= (uint64_t) ((*pptr)[1]) << 32;
- *pptr += 2;
- *r = x;
- }
-
- // Returns the current cumulative frequency (map it to a symbol yourself!)
- static inline uint32_t Rans64DecGet(Rans64State* 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 Rans64DecAdvance(Rans64State* r, uint32_t** pptr, uint32_t start, uint32_t freq, uint32_t scale_bits)
- {
- uint64_t mask = (1ull << scale_bits) - 1;
-
- // s, x = D(x)
- uint64_t x = *r;
- x = freq * (x >> scale_bits) + (x & mask) - start;
-
- // renormalize
- if (x < RANS64_L) {
- x = (x << 32) | **pptr;
- *pptr += 1;
- Rans64Assert(x >= RANS64_L);
- }
-
- *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 {
- uint64_t rcp_freq; // Fixed-point reciprocal frequency
- uint32_t freq; // Symbol frequency
- uint32_t bias; // Bias
- uint32_t cmpl_freq; // Complement of frequency: (1 << scale_bits) - freq
- uint32_t rcp_shift; // Reciprocal shift
- } Rans64EncSymbol;
-
- // Decoder symbols are straightforward.
- typedef struct {
- uint32_t start; // Start of range.
- uint32_t freq; // Symbol frequency.
- } Rans64DecSymbol;
-
- // Initializes an encoder symbol to start "start" and frequency "freq"
- static inline void Rans64EncSymbolInit(Rans64EncSymbol* s, uint32_t start, uint32_t freq, uint32_t scale_bits)
- {
- Rans64Assert(scale_bits <= 31);
- Rans64Assert(start <= (1u << scale_bits));
- Rans64Assert(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->freq = freq;
- s->cmpl_freq = ((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=~0, rcp_shift=0.
- // This gives:
- // q = mul_hi(x, rcp_freq) >> rcp_shift
- // = mul_hi(x, (1<<64) - 1)) >> 0
- // = floor(x - x/(2^64))
- // = x - 1 if 1 <= x < 2^64
- // 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 = ~0ull;
- 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;
- uint64_t x0, x1, t0, t1;
- while (freq > (1u << shift))
- shift++;
-
- // long divide ((uint128) (1 << (shift + 63)) + freq-1) / freq
- // by splitting it into two 64:64 bit divides (this works because
- // the dividend has a simple form.)
- x0 = freq - 1;
- x1 = 1ull << (shift + 31);
-
- t1 = x1 / freq;
- x0 += (x1 % freq) << 32;
- t0 = x0 / freq;
-
- s->rcp_freq = t0 + (t1 << 32);
- 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 Rans64DecSymbolInit(Rans64DecSymbol* s, uint32_t start, uint32_t freq)
- {
- Rans64Assert(start <= (1 << 31));
- Rans64Assert(freq <= (1 << 31) - start);
- s->start = start;
- s->freq = 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 Rans64EncPutSymbol(Rans64State* r, uint32_t** pptr, Rans64EncSymbol const* sym, uint32_t scale_bits)
- {
- Rans64Assert(sym->freq != 0); // can't encode symbol with freq=0
-
- // renormalize
- uint64_t x = *r;
- uint64_t x_max = ((RANS64_L >> scale_bits) << 32) * sym->freq; // turns into a shift
- if (x >= x_max) {
- *pptr -= 1;
- **pptr = (uint32_t) x;
- x >>= 32;
- }
-
- // x = C(s,x)
- uint64_t q = Rans64MulHi(x, sym->rcp_freq) >> sym->rcp_shift;
- *r = x + sym->bias + q * sym->cmpl_freq;
- }
-
- // Equivalent to RansDecAdvance that takes a symbol.
- static inline void Rans64DecAdvanceSymbol(Rans64State* r, uint32_t** pptr, Rans64DecSymbol const* sym, uint32_t scale_bits)
- {
- Rans64DecAdvance(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 Rans64DecAdvanceStep(Rans64State* r, uint32_t start, uint32_t freq, uint32_t scale_bits)
- {
- uint64_t mask = (1u << scale_bits) - 1;
-
- // s, x = D(x)
- uint64_t x = *r;
- *r = freq * (x >> scale_bits) + (x & mask) - start;
- }
-
- // Equivalent to RansDecAdvanceStep that takes a symbol.
- static inline void Rans64DecAdvanceSymbolStep(Rans64State* r, Rans64DecSymbol const* sym, uint32_t scale_bits)
- {
- Rans64DecAdvanceStep(r, sym->start, sym->freq, scale_bits);
- }
-
- // Renormalize.
- static inline void Rans64DecRenorm(Rans64State* r, uint32_t** pptr)
- {
- // renormalize
- uint64_t x = *r;
- if (x < RANS64_L) {
- x = (x << 32) | **pptr;
- *pptr += 1;
- Rans64Assert(x >= RANS64_L);
- }
-
- *r = x;
- }
-
- #endif // RANS64_HEADER
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