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