log.c File Reference

Implementation of log for the accum type. More...

#include "stdfix-full-iso.h"
#include "assert.h"
#include "arm_acle.h"

Functions
static int32_t	divide_ck (int32_t x, uint32_t k)
	This function divides x by k/64.
static uint32_t	uint32_round (uint32_t r, uint32_t n)
	Shift away a given number of bits, with rounding.
static int32_t	subtract_mult_log2 (int32_t r, int32_t x)
	This function performs a multiply-accumulate.
static int32_t	cubic_term (int32_t r)
	Computes the cubic term for log_1_2()
static uint32_t	log_1_2 (uint32_t x)
	This function calculates a range-reduced log function.
static int32_t	logkbits (int32_t x)
	This function calculates the internal representation of the log function.
accum	logk (accum x)
	Logarithm: log(x) for the accum type (s16.15).

Variables
static uint32_t	log_ck []
static int16_t	recip_table []
	Reciprocal table.

Detailed Description

Implementation of log for the accum type.

The details of the algorithm are from "Elementary Functions: Algorithms and Implemenation", 2nd edn, Jean-Michel Muller, Birkhauser, 2006.

Author

Dave Lester (david.nosp@m..r.l.nosp@m.ester.nosp@m.@man.nosp@m.chest.nosp@m.er.a.nosp@m.c.uk)

Copyright

Copyright (c) Dave Lester, Jamie Knight and The University of Manchester, 2013. All rights reserved. SpiNNaker Project Advanced Processor Technologies Group School of Computer Science The University of Manchester Manchester M13 9PL, UK

Date

30 September, 2014

Function Documentation

divide_ck()

static int32_t divide_ck ( int32_t  x, uint32_t  k  )

inlinestatic

This function divides x by k/64.

Parameters

[in]	x	input value
[in]	k	the ‘breakpoint’ index.

Returns

x/(k/64)

uint32_round()

static uint32_t uint32_round ( uint32_t  r, uint32_t  n  )

inlinestatic

Shift away a given number of bits, with rounding.

Parameters

[in]	r	The number to be rounded.
[in]	n	The number of least-significant bits to remove. Should be a constant for efficiency.

Returns

the rounded number

subtract_mult_log2()

static int32_t subtract_mult_log2 ( int32_t  r, int32_t  x  )

inlinestatic

This function performs a multiply-accumulate.

Parameters

[in]	r	accumulator value
[in]	x	one of the factors

Returns

\( r - x * log(2) \)

cubic_term()

static int32_t cubic_term ( int32_t  r )

inlinestatic

Computes the cubic term for log_1_2()

Parameters

[in]

r

an s0.31 representation of the x/ck

Returns

\( 44739601/2^{29} * r^3 \)

log_1_2()

static uint32_t log_1_2 ( uint32_t  x )

inlinestatic

This function calculates a range-reduced log function.

Parameters

[in]

x

a u0.31 fraction.

Returns

A value representing log(1+x) in u5.27 (or s4.27) format.

logkbits()

static int32_t logkbits ( int32_t  x )

inlinestatic

This function calculates the internal representation of the log function.

Parameters

[in]

x

a positive signed accum, in integer form.

Returns

A value representing log(x) (in integer form of signed accum).

logk()

accum logk

(

s1615

x

)

Logarithm: log(x) for the accum type (s16.15).

Parameters

[in]

x

Value to compute the logarithm of as an accum

Returns

The logarithm of x in accum format

Variable Documentation

log_ck

uint32_t log_ck[]

static

Initial value:

= {
      1610612736, 1612693673, 1614742838, 1616761188,
      1618749635, 1620709053, 1622640276, 1624544106,
      1626421307, 1628272616, 1630098736, 1631900343,
      1633678087, 1635432592, 1637164458, 1638874261,
      1640562556, 1642229879, 1643876743, 1645503644,
      1647111061, 1648699455, 1650269271, 1651820939,
      1653354872, 1654871473, 1656371128, 1657854212,
      1659321087, 1660772103, 1662207601, 1663627908,
      1665033342, 1666424211, 1667800815, 1669163444,
      1670512377, 1671847888, 1673170241, 1674479692,
      1675776492, 1677060882, 1678333097, 1679593367,
      1680841913, 1682078952, 1683304693, 1684519341,
      1685723096, 1686916150, 1688098693, 1689270907,
      1690432973, 1691585063, 1692727349, 1693859995,
      1694983162, 1696097009, 1697201687, 1698297348,
      1699384138, 1700462197, 1701531667, 1702592682,
      1703645376
}

\( ck = 1 + k/64 \)

Thus \( log_ck[k] = log(1 + k/64) + 12 \) in u5.27

recip_table

int16_t recip_table[]

static

Initial value:

= {
      0,  -1008,  -1986,  -2934,  -3855,  -4749,  -5617,  -6461,
      -7282,  -8080,  -8856,  -9612, -10348, -11065, -11763, -12444,
     -13107, -13754, -14386, -15002, -15604, -16191, -16765, -17326,
     -17873, -18409, -18933, -19445, -19946, -20436, -20916, -21385,
     -21845, -22296, -22737, -23169, -23593, -24008, -24415, -24815,
     -25206, -25590, -25967, -26337, -26700, -27056, -27406, -27749,
     -28087, -28418, -28744, -29064, -29378, -29687, -29991, -30290,
     -30583, -30872, -31156, -31436, -31711, -31982, -32248, -32510,
     -32768
}

Reciprocal table.