#!/bin/sh

#

# intgamma.sh

#

# Last changed in libpng 1.6.0 [February 14, 2013]

#

# COPYRIGHT: Written by John Cunningham Bowler, 2013.

# To the extent possible under law, the author has waived all copyright and

# related or neighboring rights to this work. This work is published from:

# United States.

#

# Shell script to generate png.c 8-bit and 16-bit log tables (see the code in

# png.c for details).

#

# This script uses the "bc" arbitrary precision calculator to calculate 32-bit

# fixed point values of logarithms appropriate to finding the log of an 8-bit

# (0..255) value and a similar table for the exponent calculation.

#

# "bc" must be on the path when the script is executed, and the math library

# (-lm) must be available

#

# function to print out a list of numbers as integers; the function truncates

# the integers which must be one-per-line

function print(){

}

#

# The logarithm table.

cat <<END

/* 8-bit log table: png_8bit_l2[128]

* This is a table of -log(value/255)/log(2) for 'value' in the range 128 to

* 255, so it's the base 2 logarithm of a normalized 8-bit floating point

* mantissa. The numbers are 32-bit fractions.

*/

static const png_uint_32

png_8bit_l2[128] =

{

END

#

bc -lqws <<END | print

f=65536*65536/l(2)

for (i=128;i<256;++i) { .5 - l(i/255)*f; }

END

echo '};'

echo

#

# The exponent table.

cat <<END

/* The 'exp()' case must invert the above, taking a 20-bit fixed point

* logarithmic value and returning a 16 or 8-bit number as appropriate. In

* each case only the low 16 bits are relevant - the fraction - since the

* integer bits (the top 4) simply determine a shift.

*

* The worst case is the 16-bit distinction between 65535 and 65534; this

* requires perhaps spurious accuracy in the decoding of the logarithm to

* distinguish log2(65535/65534.5) - 10^-5 or 17 bits. There is little chance

* of getting this accuracy in practice.

*

* To deal with this the following exp() function works out the exponent of the

* frational part of the logarithm by using an accurate 32-bit value from the

* top four fractional bits then multiplying in the remaining bits.

*/

static const png_uint_32

png_32bit_exp[16] =

{

END

#

bc -lqws <<END | print

f=l(2)/16

for (i=0;i<16;++i) {

x = .5 + e(-i*f)*2^32;

if (x >= 2^32) x = 2^32-1;

x;

}

END

echo '};'

echo

#

# And the table of adjustment values.

cat <<END

/* Adjustment table; provided to explain the numbers in the code below. */

#if 0

END

bc -lqws <<END | awk '{ printf "%5d %s\n", 12-NR, $0 }'

for (i=11;i>=0;--i){

(1 - e(-(2^i)/65536*l(2))) * 2^(32-i)

}

END

echo '#endif'