109 lines
2.8 KiB
Bash
109 lines
2.8 KiB
Bash
#!/bin/sh
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# intgamma.sh
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#
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# COPYRIGHT: Written by John Cunningham Bowler, 2013.
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# To the extent possible under law, the author has waived all copyright and
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# related or neighboring rights to this work. The author published this work
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# from the United States.
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#
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# Shell script to generate png.c 8-bit and 16-bit log tables (see the code in
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# png.c for details).
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#
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# This script uses the "bc" arbitrary precision calculator to calculate 32-bit
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# fixed point values of logarithms appropriate to finding the log of an 8-bit
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# (0..255) value and a similar table for the exponent calculation.
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#
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# "bc" must be on the path when the script is executed, and the math library
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# (-lm) must be available.
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# Function to print out a list of numbers as integers; the function truncates
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# the integers which must be one-per-line.
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function print(){
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awk 'BEGIN{
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str = ""
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}
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{
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sub("\\.[0-9]*$", "")
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if ($0 == "")
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$0 = "0"
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if (str == "")
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t = " " $0 "U"
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else
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t = str ", " $0 "U"
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if (length(t) >= 80) {
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print str ","
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str = " " $0 "U"
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} else
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str = t
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}
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END{
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print str
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}'
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}
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#
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# The logarithm table.
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cat <<END
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/* 8-bit log table: png_8bit_l2[128]
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* This is a table of -log(value/255)/log(2) for 'value' in the range 128 to
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* 255, so it's the base 2 logarithm of a normalized 8-bit floating point
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* mantissa. The numbers are 32-bit fractions.
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*/
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static const png_uint_32
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png_8bit_l2[128] =
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{
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END
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#
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bc -lqws <<END | print
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f=65536*65536/l(2)
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for (i=128;i<256;++i) { .5 - l(i/255)*f; }
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END
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echo '};'
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echo
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#
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# The exponent table.
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cat <<END
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/* The 'exp()' case must invert the above, taking a 20-bit fixed point
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* logarithmic value and returning a 16 or 8-bit number as appropriate. In
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* each case only the low 16 bits are relevant - the fraction - since the
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* integer bits (the top 4) simply determine a shift.
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*
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* The worst case is the 16-bit distinction between 65535 and 65534; this
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* requires perhaps spurious accuracy in the decoding of the logarithm to
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* distinguish log2(65535/65534.5) - 10^-5 or 17 bits. There is little chance
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* of getting this accuracy in practice.
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*
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* To deal with this the following exp() function works out the exponent of the
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* frational part of the logarithm by using an accurate 32-bit value from the
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* top four fractional bits then multiplying in the remaining bits.
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*/
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static const png_uint_32
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png_32bit_exp[16] =
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{
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END
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#
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bc -lqws <<END | print
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f=l(2)/16
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for (i=0;i<16;++i) {
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x = .5 + e(-i*f)*2^32;
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if (x >= 2^32) x = 2^32-1;
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x;
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}
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END
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echo '};'
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echo
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#
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# And the table of adjustment values.
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cat <<END
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/* Adjustment table; provided to explain the numbers in the code below. */
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#if 0
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END
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bc -lqws <<END | awk '{ printf "%5d %s\n", 12-NR, $0 }'
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for (i=11;i>=0;--i){
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(1 - e(-(2^i)/65536*l(2))) * 2^(32-i)
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}
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END
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echo '#endif'
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