SphinxBase  5prealpha
logmath.h File Reference

Fast integer logarithmic addition operations. More...

#include <sphinxbase/sphinxbase_export.h>
#include <sphinxbase/prim_type.h>
#include <sphinxbase/cmd_ln.h>

Go to the source code of this file.

Data Structures

struct  logadd_s
 

Macros

#define LOGMATH_TABLE(lm)   ((logadd_t *)lm)
 Obtain the log-add table from a logmath_t *.
 

Typedefs

typedef struct logadd_s logadd_t
 Integer log math computation table. More...
 
typedef struct logmath_s logmath_t
 Integer log math computation class.
 

Functions

SPHINXBASE_EXPORT logmath_tlogmath_init (float64 base, int shift, int use_table)
 Initialize a log math computation table. More...
 
SPHINXBASE_EXPORT logmath_tlogmath_read (const char *filename)
 Memory-map (or read) a log table from a file.
 
SPHINXBASE_EXPORT int32 logmath_write (logmath_t *lmath, const char *filename)
 Write a log table to a file.
 
SPHINXBASE_EXPORT int32 logmath_get_table_shape (logmath_t *lmath, uint32 *out_size, uint32 *out_width, uint32 *out_shift)
 Get the log table size and dimensions.
 
SPHINXBASE_EXPORT float64 logmath_get_base (logmath_t *lmath)
 Get the log base.
 
SPHINXBASE_EXPORT int logmath_get_zero (logmath_t *lmath)
 Get the smallest possible value represented in this base.
 
SPHINXBASE_EXPORT int logmath_get_width (logmath_t *lmath)
 Get the width of the values in a log table.
 
SPHINXBASE_EXPORT int logmath_get_shift (logmath_t *lmath)
 Get the shift of the values in a log table.
 
SPHINXBASE_EXPORT logmath_tlogmath_retain (logmath_t *lmath)
 Retain ownership of a log table. More...
 
SPHINXBASE_EXPORT int logmath_free (logmath_t *lmath)
 Free a log table. More...
 
SPHINXBASE_EXPORT int logmath_add_exact (logmath_t *lmath, int logb_p, int logb_q)
 Add two values in log space exactly and slowly (without using add table).
 
SPHINXBASE_EXPORT int logmath_add (logmath_t *lmath, int logb_p, int logb_q)
 Add two values in log space (i.e. More...
 
SPHINXBASE_EXPORT int logmath_log (logmath_t *lmath, float64 p)
 Convert linear floating point number to integer log in base B.
 
SPHINXBASE_EXPORT float64 logmath_exp (logmath_t *lmath, int logb_p)
 Convert integer log in base B to linear floating point.
 
SPHINXBASE_EXPORT int logmath_ln_to_log (logmath_t *lmath, float64 log_p)
 Convert natural log (in floating point) to integer log in base B.
 
SPHINXBASE_EXPORT float64 logmath_log_to_ln (logmath_t *lmath, int logb_p)
 Convert integer log in base B to natural log (in floating point).
 
SPHINXBASE_EXPORT int logmath_log10_to_log (logmath_t *lmath, float64 log_p)
 Convert base 10 log (in floating point) to integer log in base B.
 
SPHINXBASE_EXPORT float logmath_log10_to_log_float (logmath_t *lmath, float64 log_p)
 Convert base 10 log (in floating point) to float log in base B.
 
SPHINXBASE_EXPORT float64 logmath_log_to_log10 (logmath_t *lmath, int logb_p)
 Convert integer log in base B to base 10 log (in floating point).
 
SPHINXBASE_EXPORT float64 logmath_log_float_to_log10 (logmath_t *lmath, float log_p)
 Convert float log in base B to base 10 log.
 

Detailed Description

Fast integer logarithmic addition operations.

In evaluating HMM models, probability values are often kept in log domain, to avoid overflow. To enable these logprob values to be held in int32 variables without significant loss of precision, a logbase of (1+epsilon) (where epsilon < 0.01 or so) is used. This module maintains this logbase (B).

However, maintaining probabilities in log domain creates a problem when adding two probability values. This problem can be solved by table lookup. Note that:

  • $ b^z = b^x + b^y $
  • $ b^z = b^x(1 + b^{y-x}) = b^y(1 + e^{x-y}) $
  • $ z = x + log_b(1 + b^{y-x}) = y + log_b(1 + b^{x-y}) $

So:

  • when $ y > x, z = y + logadd\_table[-(x-y)] $
  • when $ x > y, z = x + logadd\_table[-(y-x)] $
  • where $ logadd\_table[n] = log_b(1 + b^{-n}) $

The first entry in logadd_table is simply $ log_b(2.0) $, for the case where $ y = x $ and thus $ z = log_b(2x) = log_b(2) + x $. The last entry is zero, where $ log_b(x+y) = x = y $ due to loss of precision.

Since this table can be quite large particularly for small logbases, an option is provided to compress it by dropping the least significant bits of the table.

Definition in file logmath.h.

Typedef Documentation

typedef struct logadd_s logadd_t

Integer log math computation table.

This is exposed here to allow log-add computations to be inlined.

Definition at line 93 of file logmath.h.

Function Documentation

SPHINXBASE_EXPORT int logmath_add ( logmath_t lmath,
int  logb_p,
int  logb_q 
)

Add two values in log space (i.e.

return log(exp(p)+exp(q)))

Definition at line 392 of file logmath.c.

References logmath_add_exact(), LOGMATH_TABLE, logadd_s::table, logadd_s::table_size, and logadd_s::width.

SPHINXBASE_EXPORT int logmath_free ( logmath_t lmath)

Free a log table.

Returns
new reference count (0 if freed completely)

Definition at line 342 of file logmath.c.

References ckd_free(), mmio_file_unmap(), and logadd_s::table.

Referenced by jsgf_write_fsg(), and logmath_read().

SPHINXBASE_EXPORT logmath_t* logmath_init ( float64  base,
int  shift,
int  use_table 
)

Initialize a log math computation table.

Parameters
baseThe base B in which computation is to be done.
shiftLog values are shifted right by this many bits.
use_tableWhether to use an add table or not
Returns
The newly created log math table.

Definition at line 62 of file logmath.c.

References ckd_calloc, E_ERROR, logadd_s::shift, logadd_s::table, logadd_s::table_size, and logadd_s::width.

Referenced by jsgf_write_fsg().

SPHINXBASE_EXPORT logmath_t* logmath_retain ( logmath_t lmath)

Retain ownership of a log table.

Returns
pointer to retained log table.

Definition at line 335 of file logmath.c.