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-#!/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(){
- awk 'BEGIN{
- str = ""
- }
- {
- sub("\\.[0-9]*$", "")
- if ($0 == "")
- $0 = "0"
-
- if (str == "")
- t = " " $0 "U"
- else
- t = str ", " $0 "U"
-
- if (length(t) >= 80) {
- print str ","
- str = " " $0 "U"
- } else
- str = t
- }
- END{
- print str
- }'
-}
-#
-# 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'