1 | /* makesRGB.c -- build sRGB-to-linear and linear-to-sRGB conversion tables
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2 | *
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3 | * Last changed in libpng 1.6.0 [February 14, 2013]
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4 | *
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5 | * COPYRIGHT: Written by John Cunningham Bowler, 2013.
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6 | * To the extent possible under law, the author has waived all copyright and
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7 | * related or neighboring rights to this work. This work is published from:
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8 | * United States.
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9 | *
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10 | * Make a table to convert 8-bit sRGB encoding values into the closest 16-bit
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11 | * linear value.
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12 | *
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13 | * Make two tables to take a linear value scaled to 255*65535 and return an
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14 | * approximation to the 8-bit sRGB encoded value. Calculate the error in these
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15 | * tables and display it.
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16 | */
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17 | #define _C99_SOURCE 1
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18 | #include <stdio.h>
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19 | #include <math.h>
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20 | #include <stdlib.h>
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21 |
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22 | /* pngpriv.h includes the definition of 'PNG_sRGB_FROM_LINEAR' which is required
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23 | * to verify the actual code.
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24 | */
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25 | #include "../../pngpriv.h"
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26 |
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27 | #include "sRGB.h"
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28 |
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29 | /* The tables are declared 'const' in pngpriv.h, so this redefines the tables to
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30 | * be used.
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31 | */
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32 | #define png_sRGB_table sRGB_table
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33 | #define png_sRGB_base sRGB_base
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34 | #define png_sRGB_delta sRGB_delta
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35 |
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36 | static png_uint_16 png_sRGB_table[256];
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37 | static png_uint_16 png_sRGB_base[512];
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38 | static png_byte png_sRGB_delta[512];
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39 |
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40 | static const unsigned int max_input = 255*65535;
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41 |
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42 | double
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43 | fsRGB(double l)
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44 | {
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45 | return sRGB_from_linear(l/max_input);
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46 | }
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47 |
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48 | double
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49 | sRGB(unsigned int i)
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50 | {
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51 | return fsRGB(i);
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52 | }
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53 |
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54 | double
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55 | finvsRGB(unsigned int i)
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56 | {
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57 | return 65535 * linear_from_sRGB(i/255.);
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58 | }
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59 |
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60 | png_uint_16
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61 | invsRGB(unsigned int i)
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62 | {
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63 | unsigned int x = nearbyint(finvsRGB(i));
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64 |
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65 | if (x > 65535)
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66 | {
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67 | fprintf(stderr, "invsRGB(%u) overflows to %u\n", i, x);
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68 | exit(1);
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69 | }
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70 |
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71 | return (png_uint_16)x;
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72 | }
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73 |
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74 | int
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75 | main(int argc, char **argv)
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76 | {
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77 | unsigned int i, i16, ibase;
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78 | double min_error = 0;
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79 | double max_error = 0;
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80 | double min_error16 = 0;
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81 | double max_error16 = 0;
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82 | double adjust;
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83 | double adjust_lo = 0.4, adjust_hi = 0.6, adjust_mid = 0.5;
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84 | unsigned int ec_lo = 0, ec_hi = 0, ec_mid = 0;
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85 | unsigned int error_count = 0;
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86 | unsigned int error_count16 = 0;
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87 | int test_only = 0;
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88 |
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89 | if (argc > 1)
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90 | test_only = strcmp("--test", argv[1]) == 0;
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91 |
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92 | /* Initialize the encoding table first. */
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93 | for (i=0; i<256; ++i)
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94 | {
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95 | png_sRGB_table[i] = invsRGB(i);
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96 | }
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97 |
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98 | /* Now work out the decoding tables (this is where the error comes in because
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99 | * there are 512 set points and 512 straight lines between them.)
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100 | */
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101 | for (;;)
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102 | {
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103 | if (ec_lo == 0)
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104 | adjust = adjust_lo;
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105 |
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106 | else if (ec_hi == 0)
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107 | adjust = adjust_hi;
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108 |
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109 | else if (ec_mid == 0)
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110 | adjust = adjust_mid;
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111 |
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112 | else if (ec_mid < ec_hi)
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113 | adjust = (adjust_mid + adjust_hi)/2;
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114 |
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115 | else if (ec_mid < ec_lo)
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116 | adjust = (adjust_mid + adjust_lo)/2;
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117 |
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118 | else
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119 | {
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120 | fprintf(stderr, "not reached: %u .. %u .. %u\n", ec_lo, ec_mid, ec_hi);
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121 | exit(1);
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122 | }
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123 |
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124 | /* Calculate the table using the current 'adjust' */
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125 | for (i=0; i<=511; ++i)
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126 | {
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127 | double lo = 255 * sRGB(i << 15);
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128 | double hi = 255 * sRGB((i+1) << 15);
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129 | unsigned int calc;
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130 |
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131 | calc = nearbyint((lo+adjust) * 256);
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132 | if (calc > 65535)
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133 | {
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134 | fprintf(stderr, "table[%d][0]: overflow %08x (%d)\n", i, calc,
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135 | calc);
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136 | exit(1);
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137 | }
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138 | png_sRGB_base[i] = calc;
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139 |
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140 | calc = nearbyint((hi-lo) * 32);
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141 | if (calc > 255)
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142 | {
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143 | fprintf(stderr, "table[%d][1]: overflow %08x (%d)\n", i, calc,
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144 | calc);
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145 | exit(1);
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146 | }
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147 | png_sRGB_delta[i] = calc;
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148 | }
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149 |
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150 | /* Check the 16-bit linear values alone: */
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151 | error_count16 = 0;
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152 | for (i16=0; i16 <= 65535; ++i16)
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153 | {
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154 | unsigned int i = 255*i16;
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155 | unsigned int iexact = nearbyint(255*sRGB(i));
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156 | unsigned int icalc = PNG_sRGB_FROM_LINEAR(i);
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157 |
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158 | if (icalc != iexact)
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159 | ++error_count16;
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160 | }
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161 |
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162 | /* Now try changing the adjustment. */
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163 | if (ec_lo == 0)
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164 | ec_lo = error_count16;
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165 |
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166 | else if (ec_hi == 0)
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167 | ec_hi = error_count16;
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168 |
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169 | else if (ec_mid == 0)
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170 | {
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171 | ec_mid = error_count16;
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172 | printf("/* initial error counts: %u .. %u .. %u */\n", ec_lo, ec_mid,
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173 | ec_hi);
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174 | }
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175 |
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176 | else if (error_count16 < ec_mid)
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177 | {
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178 | printf("/* adjust (mid ): %f: %u -> %u */\n", adjust, ec_mid,
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179 | error_count16);
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180 | ec_mid = error_count16;
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181 | adjust_mid = adjust;
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182 | }
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183 |
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184 | else if (adjust < adjust_mid && error_count16 < ec_lo)
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185 | {
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186 | printf("/* adjust (low ): %f: %u -> %u */\n", adjust, ec_lo,
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187 | error_count16);
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188 | ec_lo = error_count16;
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189 | adjust_lo = adjust;
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190 | }
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191 |
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192 | else if (adjust > adjust_mid && error_count16 < ec_hi)
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193 | {
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194 | printf("/* adjust (high): %f: %u -> %u */\n", adjust, ec_hi,
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195 | error_count16);
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196 | ec_hi = error_count16;
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197 | adjust_hi = adjust;
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198 | }
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199 |
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200 | else
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201 | {
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202 | adjust = adjust_mid;
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203 | printf("/* adjust: %f: %u */\n", adjust, ec_mid);
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204 | break;
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205 | }
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206 | }
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207 |
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208 | /* For each entry in the table try to adjust it to minimize the error count
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209 | * in that entry. Each entry corresponds to 128 input values.
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210 | */
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211 | for (ibase=0; ibase<65536; ibase+=128)
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212 | {
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213 | png_uint_16 base = png_sRGB_base[ibase >> 7], trybase = base, ob=base;
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214 | png_byte delta = png_sRGB_delta[ibase >> 7], trydelta = delta, od=delta;
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215 | unsigned int ecbase = 0, eco;
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216 |
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217 | for (;;)
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218 | {
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219 | png_sRGB_base[ibase >> 7] = trybase;
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220 | png_sRGB_delta[ibase >> 7] = trydelta;
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221 |
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222 | /* Check the 16-bit linear values alone: */
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223 | error_count16 = 0;
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224 | for (i16=ibase; i16 < ibase+128; ++i16)
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225 | {
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226 | unsigned int i = 255*i16;
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227 | unsigned int iexact = nearbyint(255*sRGB(i));
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228 | unsigned int icalc = PNG_sRGB_FROM_LINEAR(i);
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229 |
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230 | if (icalc != iexact)
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231 | ++error_count16;
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232 | }
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233 |
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234 | if (error_count16 == 0)
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235 | break;
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236 |
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237 | if (ecbase == 0)
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238 | {
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239 | eco = ecbase = error_count16;
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240 | ++trybase; /* First test */
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241 | }
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242 |
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243 | else if (error_count16 < ecbase)
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244 | {
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245 | if (trybase > base)
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246 | {
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247 | base = trybase;
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248 | ++trybase;
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249 | }
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250 | else if (trybase < base)
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251 | {
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252 | base = trybase;
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253 | --trybase;
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254 | }
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255 | else if (trydelta > delta)
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256 | {
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257 | delta = trydelta;
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258 | ++trydelta;
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259 | }
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260 | else if (trydelta < delta)
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261 | {
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262 | delta = trydelta;
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263 | --trydelta;
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264 | }
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265 | else
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266 | {
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267 | fprintf(stderr, "makesRGB: impossible\n");
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268 | exit(1);
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269 | }
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270 | ecbase = error_count16;
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271 | }
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272 |
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273 | else
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274 | {
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275 | if (trybase > base)
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276 | trybase = base-1;
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277 | else if (trybase < base)
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278 | {
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279 | trybase = base;
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280 | ++trydelta;
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281 | }
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282 | else if (trydelta > delta)
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283 | trydelta = delta-1;
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284 | else if (trydelta < delta)
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285 | break; /* end of tests */
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286 | }
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287 | }
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288 |
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289 | png_sRGB_base[ibase >> 7] = base;
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290 | png_sRGB_delta[ibase >> 7] = delta;
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291 | if (base != ob || delta != od)
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292 | {
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293 | printf("/* table[%u]={%u,%u} -> {%u,%u} %u -> %u errors */\n",
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294 | ibase>>7, ob, od, base, delta, eco, ecbase);
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295 | }
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296 | else if (0)
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297 | printf("/* table[%u]={%u,%u} %u errors */\n", ibase>>7, ob, od,
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298 | ecbase);
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299 | }
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300 |
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301 | /* Only do the full (slow) test at the end: */
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302 | min_error = -.4999;
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303 | max_error = .4999;
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304 | error_count = 0;
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305 |
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306 | for (i=0; i <= max_input; ++i)
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307 | {
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308 | unsigned int iexact = nearbyint(255*sRGB(i));
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309 | unsigned int icalc = PNG_sRGB_FROM_LINEAR(i);
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310 |
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311 | if (icalc != iexact)
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312 | {
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313 | double err = 255*sRGB(i) - icalc;
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314 |
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315 | if (err > (max_error+.001) || err < (min_error-.001))
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316 | {
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317 | printf(
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318 | "/* 0x%08x: exact: %3d, got: %3d [tables: %08x, %08x] (%f) */\n",
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319 | i, iexact, icalc, png_sRGB_base[i>>15],
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320 | png_sRGB_delta[i>>15], err);
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321 | }
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322 |
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323 | ++error_count;
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324 | if (err > max_error)
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325 | max_error = err;
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326 | else if (err < min_error)
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327 | min_error = err;
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328 | }
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329 | }
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330 |
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331 | /* Re-check the 16-bit cases too, including the warning if there is an error
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332 | * bigger than 1.
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333 | */
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334 | error_count16 = 0;
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335 | max_error16 = 0;
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336 | min_error16 = 0;
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337 | for (i16=0; i16 <= 65535; ++i16)
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338 | {
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339 | unsigned int i = 255*i16;
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340 | unsigned int iexact = nearbyint(255*sRGB(i));
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341 | unsigned int icalc = PNG_sRGB_FROM_LINEAR(i);
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342 |
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343 | if (icalc != iexact)
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344 | {
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345 | double err = 255*sRGB(i) - icalc;
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346 |
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347 | ++error_count16;
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348 | if (err > max_error16)
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349 | max_error16 = err;
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350 | else if (err < min_error16)
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351 | min_error16 = err;
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352 |
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353 | if (abs(icalc - iexact) > 1)
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354 | printf(
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355 | "/* 0x%04x: exact: %3d, got: %3d [tables: %08x, %08x] (%f) */\n",
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356 | i16, iexact, icalc, png_sRGB_base[i>>15],
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357 | png_sRGB_delta[i>>15], err);
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358 | }
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359 | }
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360 |
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361 | /* Check the round trip for each 8-bit sRGB value. */
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362 | for (i16=0; i16 <= 255; ++i16)
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363 | {
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364 | unsigned int i = 255 * png_sRGB_table[i16];
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365 | unsigned int iexact = nearbyint(255*sRGB(i));
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366 | unsigned int icalc = PNG_sRGB_FROM_LINEAR(i);
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367 |
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368 | if (i16 != iexact)
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369 | {
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370 | fprintf(stderr, "8-bit rounding error: %d -> %d\n", i16, iexact);
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371 | exit(1);
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372 | }
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373 |
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374 | if (icalc != i16)
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375 | {
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376 | double finv = finvsRGB(i16);
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377 |
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378 | printf("/* 8-bit roundtrip error: %d -> %f -> %d(%f) */\n",
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379 | i16, finv, icalc, fsRGB(255*finv));
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380 | }
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381 | }
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382 |
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383 |
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384 | printf("/* error: %g - %g, %u (%g%%) of readings inexact */\n",
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385 | min_error, max_error, error_count, (100.*error_count)/max_input);
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386 | printf("/* 16-bit error: %g - %g, %u (%g%%) of readings inexact */\n",
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387 | min_error16, max_error16, error_count16, (100.*error_count16)/65535);
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388 |
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389 | if (!test_only)
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390 | {
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391 | printf("const png_uint_16 png_sRGB_table[256] =\n{\n ");
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392 | for (i=0; i<255; )
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393 | {
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394 | do
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395 | {
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396 | printf("%d,", png_sRGB_table[i++]);
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397 | }
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398 | while ((i & 0x7) != 0 && i<255);
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399 | if (i<255) printf("\n ");
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400 | }
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401 | printf("%d\n};\n\n", png_sRGB_table[i]);
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402 |
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403 |
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404 | printf("const png_uint_16 png_sRGB_base[512] =\n{\n ");
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405 | for (i=0; i<511; )
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406 | {
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407 | do
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408 | {
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409 | printf("%d,", png_sRGB_base[i++]);
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410 | }
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411 | while ((i & 0x7) != 0 && i<511);
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412 | if (i<511) printf("\n ");
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413 | }
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414 | printf("%d\n};\n\n", png_sRGB_base[i]);
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415 |
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416 | printf("const png_byte png_sRGB_delta[512] =\n{\n ");
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417 | for (i=0; i<511; )
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418 | {
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419 | do
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420 | {
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421 | printf("%d,", png_sRGB_delta[i++]);
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422 | }
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423 | while ((i & 0xf) != 0 && i<511);
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424 | if (i<511) printf("\n ");
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425 | }
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426 | printf("%d\n};\n\n", png_sRGB_delta[i]);
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427 | }
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428 |
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429 | return 0;
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430 | }
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