/// Calculate the Lagarias-Miller-Odlyzko alpha tuning factor.
/// alpha = a log(x)^2 + b log(x) + c
/// a, b and c are constants that should be determined empirically.
/// @see ../doc/alpha-factor-tuning.pdf
///
double get_alpha_lmo(int128_t x)
{
double alpha = get_alpha();
// use default alpha if no command-line alpha provided
if (alpha < 1)
{
double a = 0.00156512;
double b = -0.0261411;
double c = 0.990948;
double logx = log((double) x);
alpha = a * pow(logx, 2) + b * logx + c;
}
return in_between(1, alpha, iroot<6>(x));
}
maxint_t S1(maxint_t x, int threads)
{
if (x < 1)
return 0;
if (print_status())
set_print_variables(true);
double alpha = get_alpha(x, 0.0017154, -0.0508992, 0.483613, 0.0672202);
int64_t y = (int64_t) (iroot<3>(x) * alpha);
int64_t c = PhiTiny::get_c(y);
if (x <= numeric_limits<int64_t>::max())
return S1((int64_t) x, y, c, threads);
else
return S1(x, y, c, threads);
}
void test_colors() {
printf("testing colors\n");
int r = 25;
int g = 225;
int b = 200;
int a = 255;
color c = get_color(r,g,b,a);
assert(c == 0x19E1C8FF);
assert(get_red(c) == r);
assert(get_green(c) == g);
assert(get_blue(c) == b);
assert(get_alpha(c) == a);
assert(set_red(c,0xAA) == 0xAAE1C8FF);
assert(set_green(c,0xAA) == 0x19AAC8FF);
assert(set_blue(c,0xAA) == 0x19E1AAFF);
assert(set_alpha(c,0xAA) == 0x19E1C8AA);
}
/// Calculate the Deleglise-Rivat alpha tuning factor.
/// alpha = a log(x)^3 + b log(x)^2 + c log(x) + d
/// a, b, c and d are constants that should be determined empirically.
/// @see ../doc/alpha-tuning-factor.pdf
///
double get_alpha_deleglise_rivat(int128_t x)
{
double alpha = get_alpha();
double x2 = (double) x;
// use default alpha if no command-line alpha provided
if (alpha < 1)
{
double a = 0.000356618;
double b = 0.00263762;
double c = -0.125227;
double d = 1.39952;
double logx = log(x2);
alpha = a * pow(logx, 3) + b * pow(logx, 2) + c * logx + d;
}
return in_between(1, alpha, iroot<6>(x));
}
/**
* Draws a curve for the speed graph.
*/
void GtkGraph::draw(std::queue<double> q, double height, double increment, double maxValue, const Cairo::RefPtr<Cairo::Context>& cr)
{
// wizards use computers
// computers use numbers
// no magic
double offset = increment * (m_displaySize - q.size());
cr->move_to(0, height);
for(unsigned i = 0; i< (m_displaySize - q.size());++i)
cr->line_to(i*increment, height);
double oldy;
if(q.empty()) return;
oldy = height - (q.front() * height / maxValue);
cr->line_to(offset, oldy);
q.pop();
double x = increment + offset;
while(!q.empty())
{
double y = height - (q.front() * height / maxValue);
cr->curve_to(x - increment/2, oldy, x - increment/2, y, x, y);
q.pop();
oldy = y;
x += increment;
}
if(gt::Settings::settings["GraphStyle"] == "Fill")
{
cr->stroke_preserve();
Gdk::Cairo::set_source_rgba(cr, Gdk::RGBA(gt::Settings::settings[(upl) ? "GraphUploadFillColor" : "GraphDownloadFillColor"]));
cr->line_to(x - increment, height);
cr->line_to(0,height);
auto k = Gdk::RGBA(gt::Settings::settings[(upl) ? "GraphUploadFillColor" : "GraphDownloadFillColor"]);
cr->set_source_rgba(k.get_red(), k.get_green(), k.get_blue(), k.get_alpha() * 0.5);
cr->fill();
}
else cr->stroke();
}
maxint_t S2_hard(maxint_t x, int threads)
{
if (x < 1)
return 0;
if (print_status())
set_print_variables(true);
double alpha = get_alpha(x, 0.0017154, -0.0508992, 0.483613, 0.0672202);
int64_t y = (int64_t) (iroot<3>(x) * alpha);
int64_t z = (int64_t) (x / y);
int64_t c = PhiTiny::get_c(y);
// TODO: find better S2_hard approximation formula
maxint_t s2_hard_approx = Li(x);
if (x <= numeric_limits<int64_t>::max())
return S2_hard((int64_t) x, y, z, c, (int64_t) s2_hard_approx, threads);
else
return S2_hard(x, y, z, c, s2_hard_approx, threads);
}
/// Calculate the number of primes below x using the
/// Deleglise-Rivat algorithm.
/// Run time: O(x^(2/3) / (log x)^2) operations, O(x^(1/3) * (log x)^3) space.
///
int64_t pi_deleglise_rivat_parallel1(int64_t x, int threads)
{
if (x < 2)
return 0;
double alpha = get_alpha(x, 0.0017154, -0.0508992, 0.483613, 0.0672202);
int64_t x13 = iroot<3>(x);
int64_t y = (int64_t) (x13 * alpha);
int64_t z = x / y;
int64_t p2 = P2(x, y, threads);
vector<int32_t> mu = generate_moebius(y);
vector<int32_t> lpf = generate_least_prime_factors(y);
vector<int32_t> primes = generate_primes(y);
int64_t pi_y = pi_bsearch(primes, y);
int64_t c = PhiTiny::get_c(y);
int64_t s1 = S1(x, y, c, threads);
int64_t s2 = S2(x, y, z, c, primes, lpf, mu, threads);
int64_t phi = s1 + s2;
int64_t sum = phi + pi_y - 1 - p2;
return sum;
}
int bmp_image::output_to_file(const std::string& file_name) const {
std::ofstream out(file_name.c_str(), std::ios_base::binary | std::ios_base::out);
if ( !out ) {
return 1;
}
//full header size 122
/* BMP structure
* File Header
* 0 Magic number 0x42, 0x4d (2 bytes)
* 2 File size = w*h + h*(w%4) + 122 ? (4 bytes)
* 6 Unused (4 bytes)
* 10 Pixel array offset = 122 (4 bytes)
* DIB Header
* 14 Bytes in DIB Header = 108 (4 bytes)
* 18 Bitmap width (4 bytes)
* 22 Bitmap width (4 bytes)
* 26 Color planes = 1 (2 bytes)
* 28 Bits/pixel = 32 (2 bytes)
* 30 BI_BITFIELDS = 3 (no compression used) (4 bytes)
* 34 Size of the raw data in the Pixel Array = w*h + h*(w%4) ? (incl padding) (4 bytes)
* 38 horizonal pixels/meter = 2835 (4 bytes)
* 42 vertival pixels/meter = 2835 (4 bytes)
* 46 Number of colors in the palette = 0 (4 bytes)
* 50 Important colors = 0 (4 bytes)
* 54 Red channel bit mask = 0x00FF0000 (4 bytes)
* 58 Green channel bit mask = 0x0000FF00 (4 bytes)
* 62 Blue channel bit mask = 0x000000FF (4 bytes)
* 66 Alpha channel bit mask = 0xFF000000 (4 bytes)
* 70 Color space type = 0x206E6957 ?? (4 bytes) //LCS_WINDOWS_COLOR_SPACE
* 74 CIEXYZTRIPLE Color Space (unused) (36 bytes)
* 110 red gamma = unused (4 bytes)
* 114 green gamma = unused (4 bytes)
* 118 blue gamma = unused (4 bytes)
* 122 <Pixel Data>
*/
//TODO endianess
//const boost::uint8_t unused_8 = 0;
//const boost::uint16_t unused_16 = 0;
const boost::uint32_t unused_32 = 0;
//File Header
out.write("\x42\x4d", 2); //magic number
const boost::uint32_t file_size = width*height*4 + 122;
out.write( (const char *)(&file_size), 4); //file_size
out.write( (const char *)(&unused_32), 4); //unused
const boost::uint32_t pixel_array_offset = 122;
out.write( (const char *)(&pixel_array_offset), 4); //pixel_array_offset
const boost::uint32_t dib_header_size = 108;
out.write( (const char *)(&dib_header_size), 4); //dib_header_size
const boost::uint32_t bitmap_width = width;
const boost::uint32_t bitmap_height = height;
out.write( (const char *)(&bitmap_width), 4); //bitmap_width
out.write( (const char *)(&bitmap_height), 4); //bitmap_height
const boost::uint16_t color_planes = 1;
out.write( (const char *)(&color_planes), 2); //color_planes
const boost::uint16_t bits_per_pixel = 32;
out.write( (const char *)(&bits_per_pixel), 2); //bits_per_pixel
const boost::uint32_t bitfields = 3;
out.write( (const char *)(&bitfields), 4); //bitfields
const boost::uint32_t pixel_array_size = width*height*4;
out.write( (const char *)(&pixel_array_size), 4); //pixel_array_size
const boost::uint32_t horizontal_physical_resolution = 2835;
const boost::uint32_t vertical_physical_resolution = 2835;
out.write( (const char *)(&horizontal_physical_resolution), 4); //horizontal_physical_resolution
out.write( (const char *)(&vertical_physical_resolution), 4); //vertical_physical_resolution
out.write( (const char *)(&unused_32), 4); //num of colors on palette
out.write( (const char *)(&unused_32), 4); //num of important colors
const boost::uint32_t red_channel_bit_mask = bmp_impl::endian_swap( 0x00FF0000U );
const boost::uint32_t green_channel_bit_mask = bmp_impl::endian_swap( 0x0000FF00U );
const boost::uint32_t blue_channel_bit_mask = bmp_impl::endian_swap( 0x000000FFU );
const boost::uint32_t alpha_channel_bit_mask = bmp_impl::endian_swap( 0xFF000000U );
out.write( (const char *)(&red_channel_bit_mask), 4); //red_channel_bit_mask
out.write( (const char *)(&green_channel_bit_mask), 4); //green_channel_bit_mask
out.write( (const char *)(&blue_channel_bit_mask), 4); //blue_channel_bit_mask
out.write( (const char *)(&alpha_channel_bit_mask), 4); //alpha_channel_bit_mask
const boost::uint32_t color_space_type = bmp_impl::endian_swap( 0x206E6957U );
out.write( (const char *)(&color_space_type), 4); //color_space_type
//CIEXYZTRIPLE Color Space (unused) (36 bytes)
for(unsigned i = 0; i < 36/4; ++i) {
out.write( (const char *)(&unused_32), 4);
}
out.write( (const char *)(&unused_32), 4); //red gamma
out.write( (const char *)(&unused_32), 4); //green gamma
out.write( (const char *)(&unused_32), 4); //blue gamma
for(unsigned cy = 0; cy < pixels.height(); ++cy) {
for(unsigned x = 0; x < pixels.width(); ++x) {
unsigned y = pixels.height() - cy - 1;
const single_color_t alpha = get_alpha(pixels(x, y));
const single_color_t red = get_red(pixels(x, y));
const single_color_t green = get_green(pixels(x, y));
const single_color_t blue = get_blue(pixels(x, y));
out.write((const char *)&alpha, 1);
out.write((const char *)&red, 1);
out.write((const char *)&green, 1);
out.write((const char *)&blue, 1);
}
//no padding required as the pixels themselves are 4 bytes long
}
out.close();
return 0;
}
picture
erode (picture pic, picture pen) {
raster<true_color> ras= as_raster<true_color> (pic);
raster<double> alpha= get_alpha (as_raster<true_color> (pen));
return raster_picture (erode (ras, alpha));
}
picture
outline (picture pic, picture pen) {
raster<true_color> ras= as_raster<true_color> (pic);
raster<double> alpha= get_alpha (as_raster<true_color> (pen));
return raster_picture (variation (ras, alpha));
}
static gboolean
matting_process (GeglOperation *operation,
GeglBuffer *input_buf,
GeglBuffer *aux_buf,
GeglBuffer *output_buf,
const GeglRectangle *result,
int level)
{
const GeglProperties *o = GEGL_PROPERTIES (operation);
gfloat *input = NULL;
guchar *trimap = NULL;
gfloat *output = NULL;
BufferRecord *buffer = NULL;
gboolean success = FALSE;
int w, h, i, x, y, xdiff, ydiff, neighbour_mask;
GArray *foreground_samples, *background_samples;
GArray *unknown_positions;
g_return_val_if_fail (babl_format_get_n_components (babl_format (FORMAT_INPUT )) == COMPONENTS_INPUT, FALSE);
g_return_val_if_fail (babl_format_get_n_components (babl_format (FORMAT_AUX )) == COMPONENTS_AUX, FALSE);
g_return_val_if_fail (babl_format_get_n_components (babl_format (FORMAT_OUTPUT)) == COMPONENTS_OUTPUT, FALSE);
g_return_val_if_fail (operation, FALSE);
g_return_val_if_fail (input_buf, FALSE);
g_return_val_if_fail (aux_buf, FALSE);
g_return_val_if_fail (output_buf, FALSE);
g_return_val_if_fail (result, FALSE);
w = result->width;
h = result->height;
input = g_new (gfloat, w * h * COMPONENTS_INPUT);
trimap = g_new (guchar, w * h * COMPONENTS_AUX);
output = g_new0 (gfloat, w * h * COMPONENTS_OUTPUT);
buffer = g_new0 (BufferRecord, w * h);
gegl_buffer_get (input_buf, result, 1.0, babl_format (FORMAT_INPUT), input, GEGL_AUTO_ROWSTRIDE, GEGL_ABYSS_NONE);
gegl_buffer_get ( aux_buf, result, 1.0, babl_format (FORMAT_AUX), trimap, GEGL_AUTO_ROWSTRIDE, GEGL_ABYSS_NONE);
foreground_samples = g_array_new(FALSE, FALSE, sizeof(ColorSample));
background_samples = g_array_new(FALSE, FALSE, sizeof(ColorSample));
unknown_positions = g_array_new(FALSE, FALSE, sizeof(Position));
// Get mask
for (y = 0; y < h; y++)
{
for (x = 0; x < w; x++)
{
int mask = trimap[y * w + x];
for (ydiff = -1; ydiff <= 1; ydiff++)
{
// Borders
if (y+ydiff < 0 || y+ydiff >= h)
continue;
for (xdiff = -1; xdiff <= 1; xdiff++)
{
// Borders
if (x+xdiff < 0 || x+xdiff >= w)
continue;
neighbour_mask = trimap[(y + ydiff) * w + x + xdiff];
if (neighbour_mask != mask && (mask == 0 || mask == 255))
{
int index = y*w+x;
ColorSample s;
s.pos.x = x;
s.pos.y = y;
COLOR(s.color[c] = input[index*3 + c]);
if (mask == 255)
{
g_array_append_val(foreground_samples, s);
buffer[index].fg_distance = 0;
buffer[index].bg_distance = FLT_MAX;
}
else
{
g_array_append_val(background_samples, s);
buffer[index].fg_distance = 0;
buffer[index].bg_distance = FLT_MAX;
}
// Go to next pixel
xdiff = 1;
ydiff = 1;
}
}
}
}
}
/* If we have no information to work with, there is nothing to process. */
if (foreground_samples->len == 0 ||
background_samples->len == 0)
{
success = FALSE;
goto cleanup;
}
// Initialize unknowns
for (y = 0; y < h; y++)
{
for (x = 0; x < w; x++)
{
int index = y * w + x;
if (trimap[index] != 0 && trimap[index] != 255)
{
Position p;
p.x = x;
p.y = y;
g_array_append_val(unknown_positions, p);
buffer[index].fg_distance = FLT_MAX;
buffer[index].bg_distance = FLT_MAX;
buffer[index].fg_index = rand() % foreground_samples->len;
buffer[index].bg_index = rand() % background_samples->len;
}
}
}
g_array_sort(foreground_samples, color_compare);
g_array_sort(background_samples, color_compare);
// Do real iterations
for (i = 0; i < o->iterations; i++)
{
unsigned j;
GEGL_NOTE (GEGL_DEBUG_PROCESS, "Iteration %i", i);
for (j=0; j<unknown_positions->len; j++)
{
Position p = g_array_index(unknown_positions, Position, j);
do_random_search(foreground_samples, background_samples, input, buffer, p.x, p.y, w);
}
for (j=0; j<unknown_positions->len; j++)
{
Position p = g_array_index(unknown_positions, Position, j);
do_propagate(foreground_samples, background_samples, input, buffer, trimap, p.x, p.y, w, h);
}
}
// Fill results in
for (y = 0; y < h; y++)
{
for (x = 0; x < w; x++)
{
int index = y * w + x;
if (trimap[index] == 0 || trimap[index] == 255)
{
if (trimap[index] == 0)
{
output[index] = 0;
}
else if (trimap[index] == 255)
{
output[index] = 1;
}
}
else
{
ColorSample background, foreground;
foreground = g_array_index(foreground_samples, ColorSample, buffer[index].fg_index);
background = g_array_index(background_samples, ColorSample, buffer[index].bg_index);
output[index] = get_alpha(foreground.color, background.color, &input[index * 3]);
}
}
}
// Save to buffer
gegl_buffer_set (output_buf, result, 0, babl_format (FORMAT_OUTPUT), output,
GEGL_AUTO_ROWSTRIDE);
success = TRUE;
cleanup:
g_free (input);
g_free (trimap);
g_free (output);
g_free (buffer);
g_array_free (foreground_samples, TRUE);
g_array_free (background_samples, TRUE);
g_array_free (unknown_positions, TRUE);
return success;
}