--- /dev/null
+// 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
\ No newline at end of file
projects / narabu / blobdiff