/* makesRGB.c -- build sRGB-to-linear and linear-to-sRGB conversion tables
*
* 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.
*
* Make a table to convert 8-bit sRGB encoding values into the closest 16-bit
* linear value.
*
* Make two tables to take a linear value scaled to 255*65535 and return an
* approximation to the 8-bit sRGB encoded value. Calculate the error in these
* tables and display it.
*/
#define _C99_SOURCE 1
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
/* pngpriv.h includes the definition of 'PNG_sRGB_FROM_LINEAR' which is required
* to verify the actual code.
*/
#include "../../pngpriv.h"
#include "sRGB.h"
/* The tables are declared 'const' in pngpriv.h, so this redefines the tables to
* be used.
*/
#define png_sRGB_table sRGB_table
#define png_sRGB_base sRGB_base
#define png_sRGB_delta sRGB_delta
static png_uint_16 png_sRGB_table[256];
static png_uint_16 png_sRGB_base[512];
static png_byte png_sRGB_delta[512];
static const unsigned int max_input = 255*65535;
double
fsRGB(double l)
{
return sRGB_from_linear(l/max_input);
}
double
sRGB(unsigned int i)
{
return fsRGB(i);
}
double
finvsRGB(unsigned int i)
{
return 65535 * linear_from_sRGB(i/255.);
}
png_uint_16
invsRGB(unsigned int i)
{
unsigned int x = nearbyint(finvsRGB(i));
if (x > 65535)
{
fprintf(stderr, "invsRGB(%u) overflows to %u\n", i, x);
exit(1);
}
return (png_uint_16)x;
}
int
main(int argc, char **argv)
{
unsigned int i, i16, ibase;
double min_error = 0;
double max_error = 0;
double min_error16 = 0;
double max_error16 = 0;
double adjust;
double adjust_lo = 0.4, adjust_hi = 0.6, adjust_mid = 0.5;
unsigned int ec_lo = 0, ec_hi = 0, ec_mid = 0;
unsigned int error_count = 0;
unsigned int error_count16 = 0;
int test_only = 0;
if (argc > 1)
test_only = strcmp("--test", argv[1]) == 0;
/* Initialize the encoding table first. */
for (i=0; i<256; ++i)
{
png_sRGB_table[i] = invsRGB(i);
}
/* Now work out the decoding tables (this is where the error comes in because
* there are 512 set points and 512 straight lines between them.)
*/
for (;;)
{
if (ec_lo == 0)
adjust = adjust_lo;
else if (ec_hi == 0)
adjust = adjust_hi;
else if (ec_mid == 0)
adjust = adjust_mid;
else if (ec_mid < ec_hi)
adjust = (adjust_mid + adjust_hi)/2;
else if (ec_mid < ec_lo)
adjust = (adjust_mid + adjust_lo)/2;
else
{
fprintf(stderr, "not reached: %u .. %u .. %u\n", ec_lo, ec_mid, ec_hi);
exit(1);
}
/* Calculate the table using the current 'adjust' */
for (i=0; i<=511; ++i)
{
double lo = 255 * sRGB(i << 15);
double hi = 255 * sRGB((i+1) << 15);
unsigned int calc;
calc = nearbyint((lo+adjust) * 256);
if (calc > 65535)
{
fprintf(stderr, "table[%d][0]: overflow %08x (%d)\n", i, calc,
calc);
exit(1);
}
png_sRGB_base[i] = calc;
calc = nearbyint((hi-lo) * 32);
if (calc > 255)
{
fprintf(stderr, "table[%d][1]: overflow %08x (%d)\n", i, calc,
calc);
exit(1);
}
png_sRGB_delta[i] = calc;
}
/* Check the 16-bit linear values alone: */
error_count16 = 0;
for (i16=0; i16 <= 65535; ++i16)
{
unsigned int i = 255*i16;
unsigned int iexact = nearbyint(255*sRGB(i));
unsigned int icalc = PNG_sRGB_FROM_LINEAR(i);
if (icalc != iexact)
++error_count16;
}
/* Now try changing the adjustment. */
if (ec_lo == 0)
ec_lo = error_count16;
else if (ec_hi == 0)
ec_hi = error_count16;
else if (ec_mid == 0)
{
ec_mid = error_count16;
printf("/* initial error counts: %u .. %u .. %u */\n", ec_lo, ec_mid,
ec_hi);
}
else if (error_count16 < ec_mid)
{
printf("/* adjust (mid ): %f: %u -> %u */\n", adjust, ec_mid,
error_count16);
ec_mid = error_count16;
adjust_mid = adjust;
}
else if (adjust < adjust_mid && error_count16 < ec_lo)
{
printf("/* adjust (low ): %f: %u -> %u */\n", adjust, ec_lo,
error_count16);
ec_lo = error_count16;
adjust_lo = adjust;
}
else if (adjust > adjust_mid && error_count16 < ec_hi)
{
printf("/* adjust (high): %f: %u -> %u */\n", adjust, ec_hi,
error_count16);
ec_hi = error_count16;
adjust_hi = adjust;
}
else
{
adjust = adjust_mid;
printf("/* adjust: %f: %u */\n", adjust, ec_mid);
break;
}
}
/* For each entry in the table try to adjust it to minimize the error count
* in that entry. Each entry corresponds to 128 input values.
*/
for (ibase=0; ibase<65536; ibase+=128)
{
png_uint_16 base = png_sRGB_base[ibase >> 7], trybase = base, ob=base;
png_byte delta = png_sRGB_delta[ibase >> 7], trydelta = delta, od=delta;
unsigned int ecbase = 0, eco;
for (;;)
{
png_sRGB_base[ibase >> 7] = trybase;
png_sRGB_delta[ibase >> 7] = trydelta;
/* Check the 16-bit linear values alone: */
error_count16 = 0;
for (i16=ibase; i16 < ibase+128; ++i16)
{
unsigned int i = 255*i16;
unsigned int iexact = nearbyint(255*sRGB(i));
unsigned int icalc = PNG_sRGB_FROM_LINEAR(i);
if (icalc != iexact)
++error_count16;
}
if (error_count16 == 0)
break;
if (ecbase == 0)
{
eco = ecbase = error_count16;
++trybase; /* First test */
}
else if (error_count16 < ecbase)
{
if (trybase > base)
{
base = trybase;
++trybase;
}
else if (trybase < base)
{
base = trybase;
--trybase;
}
else if (trydelta > delta)
{
delta = trydelta;
++trydelta;
}
else if (trydelta < delta)
{
delta = trydelta;
--trydelta;
}
else
{
fprintf(stderr, "makesRGB: impossible\n");
exit(1);
}
ecbase = error_count16;
}
else
{
if (trybase > base)
trybase = base-1;
else if (trybase < base)
{
trybase = base;
++trydelta;
}
else if (trydelta > delta)
trydelta = delta-1;
else if (trydelta < delta)
break; /* end of tests */
}
}
png_sRGB_base[ibase >> 7] = base;
png_sRGB_delta[ibase >> 7] = delta;
if (base != ob || delta != od)
{
printf("/* table[%u]={%u,%u} -> {%u,%u} %u -> %u errors */\n",
ibase>>7, ob, od, base, delta, eco, ecbase);
}
else if (0)
printf("/* table[%u]={%u,%u} %u errors */\n", ibase>>7, ob, od,
ecbase);
}
/* Only do the full (slow) test at the end: */
min_error = -.4999;
max_error = .4999;
error_count = 0;
for (i=0; i <= max_input; ++i)
{
unsigned int iexact = nearbyint(255*sRGB(i));
unsigned int icalc = PNG_sRGB_FROM_LINEAR(i);
if (icalc != iexact)
{
double err = 255*sRGB(i) - icalc;
if (err > (max_error+.001) || err < (min_error-.001))
{
printf(
"/* 0x%08x: exact: %3d, got: %3d [tables: %08x, %08x] (%f) */\n",
i, iexact, icalc, png_sRGB_base[i>>15],
png_sRGB_delta[i>>15], err);
}
++error_count;
if (err > max_error)
max_error = err;
else if (err < min_error)
min_error = err;
}
}
/* Re-check the 16-bit cases too, including the warning if there is an error
* bigger than 1.
*/
error_count16 = 0;
max_error16 = 0;
min_error16 = 0;
for (i16=0; i16 <= 65535; ++i16)
{
unsigned int i = 255*i16;
unsigned int iexact = nearbyint(255*sRGB(i));
unsigned int icalc = PNG_sRGB_FROM_LINEAR(i);
if (icalc != iexact)
{
double err = 255*sRGB(i) - icalc;
++error_count16;
if (err > max_error16)
max_error16 = err;
else if (err < min_error16)
min_error16 = err;
if (abs(icalc - iexact) > 1)
printf(
"/* 0x%04x: exact: %3d, got: %3d [tables: %08x, %08x] (%f) */\n",
i16, iexact, icalc, png_sRGB_base[i>>15],
png_sRGB_delta[i>>15], err);
}
}
/* Check the round trip for each 8-bit sRGB value. */
for (i16=0; i16 <= 255; ++i16)
{
unsigned int i = 255 * png_sRGB_table[i16];
unsigned int iexact = nearbyint(255*sRGB(i));
unsigned int icalc = PNG_sRGB_FROM_LINEAR(i);
if (i16 != iexact)
{
fprintf(stderr, "8-bit rounding error: %d -> %d\n", i16, iexact);
exit(1);
}
if (icalc != i16)
{
double finv = finvsRGB(i16);
printf("/* 8-bit roundtrip error: %d -> %f -> %d(%f) */\n",
i16, finv, icalc, fsRGB(255*finv));
}
}
printf("/* error: %g - %g, %u (%g%%) of readings inexact */\n",
min_error, max_error, error_count, (100.*error_count)/max_input);
printf("/* 16-bit error: %g - %g, %u (%g%%) of readings inexact */\n",
min_error16, max_error16, error_count16, (100.*error_count16)/65535);
if (!test_only)
{
printf("PNG_CONST png_uint_16 png_sRGB_table[256] =\n{\n ");
for (i=0; i<255; )
{
do
{
printf("%d,", png_sRGB_table[i++]);
}
while ((i & 0x7) != 0 && i<255);
if (i<255) printf("\n ");
}
printf("%d\n};\n\n", png_sRGB_table[i]);
printf("PNG_CONST png_uint_16 png_sRGB_base[512] =\n{\n ");
for (i=0; i<511; )
{
do
{
printf("%d,", png_sRGB_base[i++]);
}
while ((i & 0x7) != 0 && i<511);
if (i<511) printf("\n ");
}
printf("%d\n};\n\n", png_sRGB_base[i]);
printf("PNG_CONST png_byte png_sRGB_delta[512] =\n{\n ");
for (i=0; i<511; )
{
do
{
printf("%d,", png_sRGB_delta[i++]);
}
while ((i & 0xf) != 0 && i<511);
if (i<511) printf("\n ");
}
printf("%d\n};\n\n", png_sRGB_delta[i]);
}
return 0;
}