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| 1 #!/bin/sh |
| 2 # |
| 3 # intgamma.sh |
| 4 # |
| 5 # Last changed in libpng 1.6.0 [February 14, 2013] |
| 6 # |
| 7 # COPYRIGHT: Written by John Cunningham Bowler, 2013. |
| 8 # To the extent possible under law, the author has waived all copyright and |
| 9 # related or neighboring rights to this work. This work is published from: |
| 10 # United States. |
| 11 # |
| 12 # Shell script to generate png.c 8-bit and 16-bit log tables (see the code in |
| 13 # png.c for details). |
| 14 # |
| 15 # This script uses the "bc" arbitrary precision calculator to calculate 32-bit |
| 16 # fixed point values of logarithms appropriate to finding the log of an 8-bit |
| 17 # (0..255) value and a similar table for the exponent calculation. |
| 18 # |
| 19 # "bc" must be on the path when the script is executed, and the math library |
| 20 # (-lm) must be available |
| 21 # |
| 22 # function to print out a list of numbers as integers; the function truncates |
| 23 # the integers which must be one-per-line |
| 24 function print(){ |
| 25 awk 'BEGIN{ |
| 26 str = "" |
| 27 } |
| 28 { |
| 29 sub("\\.[0-9]*$", "") |
| 30 if ($0 == "") |
| 31 $0 = "0" |
| 32 |
| 33 if (str == "") |
| 34 t = " " $0 "U" |
| 35 else |
| 36 t = str ", " $0 "U" |
| 37 |
| 38 if (length(t) >= 80) { |
| 39 print str "," |
| 40 str = " " $0 "U" |
| 41 } else |
| 42 str = t |
| 43 } |
| 44 END{ |
| 45 print str |
| 46 }' |
| 47 } |
| 48 # |
| 49 # The logarithm table. |
| 50 cat <<END |
| 51 /* 8-bit log table: png_8bit_l2[128] |
| 52 * This is a table of -log(value/255)/log(2) for 'value' in the range 128 to |
| 53 * 255, so it's the base 2 logarithm of a normalized 8-bit floating point |
| 54 * mantissa. The numbers are 32-bit fractions. |
| 55 */ |
| 56 static const png_uint_32 |
| 57 png_8bit_l2[128] = |
| 58 { |
| 59 END |
| 60 # |
| 61 bc -lqws <<END | print |
| 62 f=65536*65536/l(2) |
| 63 for (i=128;i<256;++i) { .5 - l(i/255)*f; } |
| 64 END |
| 65 echo '};' |
| 66 echo |
| 67 # |
| 68 # The exponent table. |
| 69 cat <<END |
| 70 /* The 'exp()' case must invert the above, taking a 20-bit fixed point |
| 71 * logarithmic value and returning a 16 or 8-bit number as appropriate. In |
| 72 * each case only the low 16 bits are relevant - the fraction - since the |
| 73 * integer bits (the top 4) simply determine a shift. |
| 74 * |
| 75 * The worst case is the 16-bit distinction between 65535 and 65534; this |
| 76 * requires perhaps spurious accuracy in the decoding of the logarithm to |
| 77 * distinguish log2(65535/65534.5) - 10^-5 or 17 bits. There is little chance |
| 78 * of getting this accuracy in practice. |
| 79 * |
| 80 * To deal with this the following exp() function works out the exponent of the |
| 81 * frational part of the logarithm by using an accurate 32-bit value from the |
| 82 * top four fractional bits then multiplying in the remaining bits. |
| 83 */ |
| 84 static const png_uint_32 |
| 85 png_32bit_exp[16] = |
| 86 { |
| 87 END |
| 88 # |
| 89 bc -lqws <<END | print |
| 90 f=l(2)/16 |
| 91 for (i=0;i<16;++i) { |
| 92 x = .5 + e(-i*f)*2^32; |
| 93 if (x >= 2^32) x = 2^32-1; |
| 94 x; |
| 95 } |
| 96 END |
| 97 echo '};' |
| 98 echo |
| 99 # |
| 100 # And the table of adjustment values. |
| 101 cat <<END |
| 102 /* Adjustment table; provided to explain the numbers in the code below. */ |
| 103 #if 0 |
| 104 END |
| 105 bc -lqws <<END | awk '{ printf "%5d %s\n", 12-NR, $0 }' |
| 106 for (i=11;i>=0;--i){ |
| 107 (1 - e(-(2^i)/65536*l(2))) * 2^(32-i) |
| 108 } |
| 109 END |
| 110 echo '#endif' |
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