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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'