// Three-lobed Lanczos, the most common choice.
-#define LANCZOS_RADIUS 3.0
+// Note that if you change this, the accuracy for LANCZOS_TABLE_SIZE
+// needs to be recomputed.
+#define LANCZOS_RADIUS 3.0f
#include <epoxy/gl.h>
#include <assert.h>
#include <math.h>
#include <stdio.h>
#include <algorithm>
+#include <Eigen/Sparse>
+#include <Eigen/SparseQR>
+#include <Eigen/OrderingMethods>
#include "effect_chain.h"
#include "effect_util.h"
#include "fp16.h"
+#include "init.h"
#include "resample_effect.h"
#include "util.h"
+using namespace Eigen;
using namespace std;
namespace movit {
namespace {
-template<class T>
-struct Tap {
- T weight;
- T pos;
-};
-
float sinc(float x)
{
if (fabs(x) < 1e-6) {
}
}
-float lanczos_weight(float x, float a)
+float lanczos_weight(float x)
{
- if (fabs(x) > a) {
+ if (fabs(x) > LANCZOS_RADIUS) {
return 0.0f;
} else {
- return sinc(M_PI * x) * sinc(M_PI * x / a);
+ return sinc(M_PI * x) * sinc((M_PI / LANCZOS_RADIUS) * x);
+ }
+}
+
+// The weight function can be expensive to compute over and over again
+// (which will happen during e.g. a zoom), but it is also easy to interpolate
+// linearly. We compute the right half of the function (in the range of
+// 0..LANCZOS_RADIUS), with two guard elements for easier interpolation, and
+// linearly interpolate to get our function.
+//
+// We want to scale the table so that the maximum error is always smaller
+// than 1e-6. As per http://www-solar.mcs.st-andrews.ac.uk/~clare/Lectures/num-analysis/Numan_chap3.pdf,
+// the error for interpolating a function linearly between points [a,b] is
+//
+// e = 1/2 (x-a)(x-b) f''(u_x)
+//
+// for some point u_x in [a,b] (where f(x) is our Lanczos function; we're
+// assuming LANCZOS_RADIUS=3 from here on). Obviously this is bounded by
+// f''(x) over the entire range. Numeric optimization shows the maximum of
+// |f''(x)| to be in x=1.09369819474562880, with the value 2.40067758733152381.
+// So if the steps between consecutive values are called d, we get
+//
+// |e| <= 1/2 (d/2)^2 2.4007
+// |e| <= 0.1367 d^2
+//
+// Solve for e = 1e-6 yields a step size of 0.0027, which to cover the range
+// 0..3 needs 1109 steps. We round up to the next power of two, just to be sure.
+//
+// You need to call lanczos_table_init_done before the first call to
+// lanczos_weight_cached.
+#define LANCZOS_TABLE_SIZE 2048
+bool lanczos_table_init_done = false;
+float lanczos_table[LANCZOS_TABLE_SIZE + 2];
+
+void init_lanczos_table()
+{
+ for (unsigned i = 0; i < LANCZOS_TABLE_SIZE + 2; ++i) {
+ lanczos_table[i] = lanczos_weight(float(i) * (LANCZOS_RADIUS / LANCZOS_TABLE_SIZE));
}
+ lanczos_table_init_done = true;
+}
+
+float lanczos_weight_cached(float x)
+{
+ x = fabs(x);
+ if (x > LANCZOS_RADIUS) {
+ return 0.0f;
+ }
+ float table_pos = x * (LANCZOS_TABLE_SIZE / LANCZOS_RADIUS);
+ unsigned table_pos_int = int(table_pos); // Truncate towards zero.
+ float table_pos_frac = table_pos - table_pos_int;
+ assert(table_pos < LANCZOS_TABLE_SIZE + 2);
+ return lanczos_table[table_pos_int] +
+ table_pos_frac * (lanczos_table[table_pos_int + 1] - lanczos_table[table_pos_int]);
}
// Euclid's algorithm, from Wikipedia.
}
template<class DestFloat>
-unsigned combine_samples(Tap<float> *src, Tap<DestFloat> *dst, unsigned src_size, unsigned num_src_samples, unsigned max_samples_saved)
+unsigned combine_samples(const Tap<float> *src, Tap<DestFloat> *dst, float num_subtexels, float inv_num_subtexels, unsigned num_src_samples, unsigned max_samples_saved)
{
+ // Cut off near-zero values at both sides.
unsigned num_samples_saved = 0;
+ while (num_samples_saved < max_samples_saved &&
+ num_src_samples > 0 &&
+ fabs(src[0].weight) < 1e-6) {
+ ++src;
+ --num_src_samples;
+ ++num_samples_saved;
+ }
+ while (num_samples_saved < max_samples_saved &&
+ num_src_samples > 0 &&
+ fabs(src[num_src_samples - 1].weight) < 1e-6) {
+ --num_src_samples;
+ ++num_samples_saved;
+ }
+
for (unsigned i = 0, j = 0; i < num_src_samples; ++i, ++j) {
// Copy the sample directly; it will be overwritten later if we can combine.
if (dst != NULL) {
float pos2 = src[i + 1].pos;
assert(pos2 > pos1);
- fp16_int_t pos, total_weight;
+ DestFloat pos, total_weight;
float sum_sq_error;
- combine_two_samples(w1, w2, pos1, pos2, src_size, &pos, &total_weight, &sum_sq_error);
+ combine_two_samples(w1, w2, pos1, pos2, num_subtexels, inv_num_subtexels, &pos, &total_weight, &sum_sq_error);
// If the interpolation error is larger than that of about sqrt(2) of
// a level at 8-bit precision, don't combine. (You'd think 1.0 was enough,
// but since the artifacts are not really random, they can get quite
// visible. On the other hand, going to 0.25f, I can see no change at
// all with 8-bit output, so it would not seem to be worth it.)
- if (sum_sq_error > 0.5f / (256.0f * 256.0f)) {
+ if (sum_sq_error > 0.5f / (255.0f * 255.0f)) {
continue;
}
return num_samples_saved;
}
+// Normalize so that the sum becomes one. Note that we do it twice;
+// this sometimes helps a tiny little bit when we have many samples.
+template<class T>
+void normalize_sum(Tap<T>* vals, unsigned num)
+{
+ for (int normalize_pass = 0; normalize_pass < 2; ++normalize_pass) {
+ float sum = 0.0;
+ for (unsigned i = 0; i < num; ++i) {
+ sum += to_fp32(vals[i].weight);
+ }
+ float inv_sum = 1.0 / sum;
+ for (unsigned i = 0; i < num; ++i) {
+ vals[i].weight = from_fp32<T>(to_fp32(vals[i].weight) * inv_sum);
+ }
+ }
+}
+
+// Make use of the bilinear filtering in the GPU to reduce the number of samples
+// we need to make. This is a bit more complex than BlurEffect since we cannot combine
+// two neighboring samples if their weights have differing signs, so we first need to
+// figure out the maximum number of samples. Then, we downconvert all the weights to
+// that number -- we could have gone for a variable-length system, but this is simpler,
+// and the gains would probably be offset by the extra cost of checking when to stop.
+//
+// The greedy strategy for combining samples is optimal.
+template<class DestFloat>
+unsigned combine_many_samples(const Tap<float> *weights, unsigned src_size, unsigned src_samples, unsigned dst_samples, unique_ptr<Tap<DestFloat>[]> *bilinear_weights)
+{
+ float num_subtexels = src_size / movit_texel_subpixel_precision;
+ float inv_num_subtexels = movit_texel_subpixel_precision / src_size;
+
+ unsigned max_samples_saved = UINT_MAX;
+ for (unsigned y = 0; y < dst_samples && max_samples_saved > 0; ++y) {
+ unsigned num_samples_saved = combine_samples<DestFloat>(weights + y * src_samples, NULL, num_subtexels, inv_num_subtexels, src_samples, max_samples_saved);
+ max_samples_saved = min(max_samples_saved, num_samples_saved);
+ }
+
+ // Now that we know the right width, actually combine the samples.
+ unsigned src_bilinear_samples = src_samples - max_samples_saved;
+ bilinear_weights->reset(new Tap<DestFloat>[dst_samples * src_bilinear_samples]);
+ for (unsigned y = 0; y < dst_samples; ++y) {
+ Tap<DestFloat> *bilinear_weights_ptr = bilinear_weights->get() + y * src_bilinear_samples;
+ unsigned num_samples_saved = combine_samples(
+ weights + y * src_samples,
+ bilinear_weights_ptr,
+ num_subtexels,
+ inv_num_subtexels,
+ src_samples,
+ max_samples_saved);
+ assert(num_samples_saved == max_samples_saved);
+ normalize_sum(bilinear_weights_ptr, src_bilinear_samples);
+ }
+ return src_bilinear_samples;
+}
+
+// Compute the sum of squared errors between the ideal weights (which are
+// assumed to fall exactly on pixel centers) and the weights that result
+// from sampling at <bilinear_weights>. The primary reason for the difference
+// is inaccuracy in the sampling positions, both due to limited precision
+// in storing them (already inherent in sending them in as fp16_int_t)
+// and in subtexel sampling precision (which we calculate in this function).
+template<class T>
+double compute_sum_sq_error(const Tap<float>* weights, unsigned num_weights,
+ const Tap<T>* bilinear_weights, unsigned num_bilinear_weights,
+ unsigned size)
+{
+ // Find the effective range of the bilinear-optimized kernel.
+ // Due to rounding of the positions, this is not necessarily the same
+ // as the intended range (ie., the range of the original weights).
+ int lower_pos = int(floor(to_fp32(bilinear_weights[0].pos) * size - 0.5f));
+ int upper_pos = int(ceil(to_fp32(bilinear_weights[num_bilinear_weights - 1].pos) * size - 0.5f)) + 2;
+ lower_pos = min<int>(lower_pos, lrintf(weights[0].pos * size - 0.5f));
+ upper_pos = max<int>(upper_pos, lrintf(weights[num_weights - 1].pos * size - 0.5f) + 1);
+
+ float* effective_weights = new float[upper_pos - lower_pos];
+ for (int i = 0; i < upper_pos - lower_pos; ++i) {
+ effective_weights[i] = 0.0f;
+ }
+
+ // Now find the effective weights that result from this sampling.
+ for (unsigned i = 0; i < num_bilinear_weights; ++i) {
+ const float pixel_pos = to_fp32(bilinear_weights[i].pos) * size - 0.5f;
+ const int x0 = int(floor(pixel_pos)) - lower_pos;
+ const int x1 = x0 + 1;
+ const float f = lrintf((pixel_pos - (x0 + lower_pos)) / movit_texel_subpixel_precision) * movit_texel_subpixel_precision;
+
+ assert(x0 >= 0);
+ assert(x1 >= 0);
+ assert(x0 < upper_pos - lower_pos);
+ assert(x1 < upper_pos - lower_pos);
+
+ effective_weights[x0] += to_fp32(bilinear_weights[i].weight) * (1.0f - f);
+ effective_weights[x1] += to_fp32(bilinear_weights[i].weight) * f;
+ }
+
+ // Subtract the desired weights to get the error.
+ for (unsigned i = 0; i < num_weights; ++i) {
+ const int x = lrintf(weights[i].pos * size - 0.5f) - lower_pos;
+ assert(x >= 0);
+ assert(x < upper_pos - lower_pos);
+
+ effective_weights[x] -= weights[i].weight;
+ }
+
+ double sum_sq_error = 0.0;
+ for (unsigned i = 0; i < num_weights; ++i) {
+ sum_sq_error += effective_weights[i] * effective_weights[i];
+ }
+
+ delete[] effective_weights;
+ return sum_sq_error;
+}
+
} // namespace
ResampleEffect::ResampleEffect()
last_output_width(-1),
last_output_height(-1),
last_offset(0.0 / 0.0), // NaN.
- last_zoom(0.0 / 0.0) // NaN.
+ last_zoom(0.0 / 0.0), // NaN.
+ last_texture_width(-1), last_texture_height(-1)
{
register_int("direction", (int *)&direction);
register_int("input_width", &input_width);
register_int("output_height", &output_height);
register_float("offset", &offset);
register_float("zoom", &zoom);
+ register_uniform_sampler2d("sample_tex", &uniform_sample_tex);
+ register_uniform_int("num_samples", &uniform_num_samples);
+ register_uniform_float("num_loops", &uniform_num_loops);
+ register_uniform_float("slice_height", &uniform_slice_height);
+ register_uniform_float("sample_x_scale", &uniform_sample_x_scale);
+ register_uniform_float("sample_x_offset", &uniform_sample_x_offset);
+ register_uniform_float("whole_pixel_offset", &uniform_whole_pixel_offset);
glGenTextures(1, &texnum);
+
+ if (!lanczos_table_init_done) {
+ // Could in theory race between two threads if we are unlucky,
+ // but that is harmless, since they'll write the same data.
+ init_lanczos_table();
+ }
}
SingleResamplePassEffect::~SingleResamplePassEffect()
assert(false);
}
+ ScalingWeights weights = calculate_scaling_weights(src_size, dst_size, zoom, offset);
+ src_bilinear_samples = weights.src_bilinear_samples;
+ num_loops = weights.num_loops;
+ slice_height = 1.0f / weights.num_loops;
+
+ // Encode as a two-component texture. Note the GL_REPEAT.
+ glActiveTexture(GL_TEXTURE0 + *sampler_num);
+ check_error();
+ glBindTexture(GL_TEXTURE_2D, texnum);
+ check_error();
+ if (last_texture_width == -1) {
+ // Need to set this state the first time.
+ glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
+ check_error();
+ glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT);
+ check_error();
+ glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT);
+ check_error();
+ }
+
+ GLenum type, internal_format;
+ void *pixels;
+ assert((weights.bilinear_weights_fp16 == nullptr) != (weights.bilinear_weights_fp32 == nullptr));
+ if (weights.bilinear_weights_fp32 != nullptr) {
+ type = GL_FLOAT;
+ internal_format = GL_RG32F;
+ pixels = weights.bilinear_weights_fp32.get();
+ } else {
+ type = GL_HALF_FLOAT;
+ internal_format = GL_RG16F;
+ pixels = weights.bilinear_weights_fp16.get();
+ }
+
+ if (int(weights.src_bilinear_samples) == last_texture_width &&
+ int(weights.dst_samples) == last_texture_height &&
+ internal_format == last_texture_internal_format) {
+ // Texture dimensions and type are unchanged; it is more efficient
+ // to just update it rather than making an entirely new texture.
+ glTexSubImage2D(GL_TEXTURE_2D, 0, 0, 0, weights.src_bilinear_samples, weights.dst_samples, GL_RG, type, pixels);
+ } else {
+ glTexImage2D(GL_TEXTURE_2D, 0, internal_format, weights.src_bilinear_samples, weights.dst_samples, 0, GL_RG, type, pixels);
+ last_texture_width = weights.src_bilinear_samples;
+ last_texture_height = weights.dst_samples;
+ last_texture_internal_format = internal_format;
+ }
+ check_error();
+}
+
+ScalingWeights calculate_scaling_weights(unsigned src_size, unsigned dst_size, float zoom, float offset)
+{
+ if (!lanczos_table_init_done) {
+ // Only needed if run from outside ResampleEffect.
+ init_lanczos_table();
+ }
+
// For many resamplings (e.g. 640 -> 1280), we will end up with the same
// set of samples over and over again in a loop. Thus, we can compute only
// the first such loop, and then ask the card to repeat the texture for us.
// This is both easier on the texture cache and lowers our CPU cost for
// generating the kernel somewhat.
float scaling_factor;
+ int num_loops;
if (fabs(zoom - 1.0f) < 1e-6) {
num_loops = gcd(src_size, dst_size);
scaling_factor = float(dst_size) / float(src_size);
num_loops = 1;
scaling_factor = zoom * float(dst_size) / float(src_size);
}
- slice_height = 1.0f / num_loops;
unsigned dst_samples = dst_size / num_loops;
// Sample the kernel in the right place. A diagram with a triangular kernel
float radius_scaling_factor = min(scaling_factor, 1.0f);
int int_radius = lrintf(LANCZOS_RADIUS / radius_scaling_factor);
int src_samples = int_radius * 2 + 1;
- Tap<float> *weights = new Tap<float>[dst_samples * src_samples];
+ unique_ptr<Tap<float>[]> weights(new Tap<float>[dst_samples * src_samples]);
float subpixel_offset = offset - lrintf(offset); // The part not covered by whole_pixel_offset.
assert(subpixel_offset >= -0.5f && subpixel_offset <= 0.5f);
for (unsigned y = 0; y < dst_samples; ++y) {
int base_src_y = lrintf(center_src_y);
// Now sample <int_radius> pixels on each side around that point.
+ float inv_src_size = 1.0 / float(src_size);
for (int i = 0; i < src_samples; ++i) {
int src_y = base_src_y + i - int_radius;
- float weight = lanczos_weight(radius_scaling_factor * (src_y - center_src_y - subpixel_offset), LANCZOS_RADIUS);
+ float weight = lanczos_weight_cached(radius_scaling_factor * (src_y - center_src_y - subpixel_offset));
weights[y * src_samples + i].weight = weight * radius_scaling_factor;
- weights[y * src_samples + i].pos = (src_y + 0.5) / float(src_size);
+ weights[y * src_samples + i].pos = (src_y + 0.5f) * inv_src_size;
}
}
// Now make use of the bilinear filtering in the GPU to reduce the number of samples
- // we need to make. This is a bit more complex than BlurEffect since we cannot combine
- // two neighboring samples if their weights have differing signs, so we first need to
- // figure out the maximum number of samples. Then, we downconvert all the weights to
- // that number -- we could have gone for a variable-length system, but this is simpler,
- // and the gains would probably be offset by the extra cost of checking when to stop.
- //
- // The greedy strategy for combining samples is optimal.
- src_bilinear_samples = 0;
+ // we need to make. Try fp16 first; if it's not accurate enough, we go to fp32.
+ // Our tolerance level for total error is a bit higher than the one for invididual
+ // samples, since one would assume overall errors in the shape don't matter as much.
+ const float max_error = 2.0f / (255.0f * 255.0f);
+ unique_ptr<Tap<fp16_int_t>[]> bilinear_weights_fp16;
+ int src_bilinear_samples = combine_many_samples(weights.get(), src_size, src_samples, dst_samples, &bilinear_weights_fp16);
+ unique_ptr<Tap<float>[]> bilinear_weights_fp32 = NULL;
+ double max_sum_sq_error_fp16 = 0.0;
for (unsigned y = 0; y < dst_samples; ++y) {
- unsigned num_samples_saved = combine_samples<fp16_int_t>(weights + y * src_samples, NULL, src_size, src_samples, UINT_MAX);
- src_bilinear_samples = max<int>(src_bilinear_samples, src_samples - num_samples_saved);
- }
-
- // Now that we know the right width, actually combine the samples.
- Tap<fp16_int_t> *bilinear_weights = new Tap<fp16_int_t>[dst_samples * src_bilinear_samples];
- for (unsigned y = 0; y < dst_samples; ++y) {
- Tap<fp16_int_t> *bilinear_weights_ptr = bilinear_weights + y * src_bilinear_samples;
- unsigned num_samples_saved = combine_samples(
- weights + y * src_samples,
- bilinear_weights_ptr,
- src_size,
- src_samples,
- src_samples - src_bilinear_samples);
- assert(int(src_samples) - int(num_samples_saved) == src_bilinear_samples);
-
- // Normalize so that the sum becomes one. Note that we do it twice;
- // this sometimes helps a tiny little bit when we have many samples.
- for (int normalize_pass = 0; normalize_pass < 2; ++normalize_pass) {
- double sum = 0.0;
- for (int i = 0; i < src_bilinear_samples; ++i) {
- sum += fp16_to_fp64(bilinear_weights_ptr[i].weight);
- }
- for (int i = 0; i < src_bilinear_samples; ++i) {
- bilinear_weights_ptr[i].weight = fp64_to_fp16(
- fp16_to_fp64(bilinear_weights_ptr[i].weight) / sum);
- }
+ double sum_sq_error_fp16 = compute_sum_sq_error(
+ weights.get() + y * src_samples, src_samples,
+ bilinear_weights_fp16.get() + y * src_bilinear_samples, src_bilinear_samples,
+ src_size);
+ max_sum_sq_error_fp16 = std::max(max_sum_sq_error_fp16, sum_sq_error_fp16);
+ if (max_sum_sq_error_fp16 > max_error) {
+ break;
}
}
- // Encode as a two-component texture. Note the GL_REPEAT.
- glActiveTexture(GL_TEXTURE0 + *sampler_num);
- check_error();
- glBindTexture(GL_TEXTURE_2D, texnum);
- check_error();
- glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
- check_error();
- glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT);
- check_error();
- glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT);
- check_error();
- glTexImage2D(GL_TEXTURE_2D, 0, GL_RG16F, src_bilinear_samples, dst_samples, 0, GL_RG, GL_HALF_FLOAT, bilinear_weights);
- check_error();
+ if (max_sum_sq_error_fp16 > max_error) {
+ bilinear_weights_fp16.reset();
+ src_bilinear_samples = combine_many_samples(weights.get(), src_size, src_samples, dst_samples, &bilinear_weights_fp32);
+ }
- delete[] weights;
- delete[] bilinear_weights;
+ ScalingWeights ret;
+ ret.src_bilinear_samples = src_bilinear_samples;
+ ret.dst_samples = dst_samples;
+ ret.num_loops = num_loops;
+ ret.bilinear_weights_fp16 = move(bilinear_weights_fp16);
+ ret.bilinear_weights_fp32 = move(bilinear_weights_fp32);
+ return ret;
}
void SingleResamplePassEffect::set_gl_state(GLuint glsl_program_num, const string &prefix, unsigned *sampler_num)
glBindTexture(GL_TEXTURE_2D, texnum);
check_error();
- set_uniform_int(glsl_program_num, prefix, "sample_tex", *sampler_num);
+ uniform_sample_tex = *sampler_num;
++*sampler_num;
- set_uniform_int(glsl_program_num, prefix, "num_samples", src_bilinear_samples);
- set_uniform_float(glsl_program_num, prefix, "num_loops", num_loops);
- set_uniform_float(glsl_program_num, prefix, "slice_height", slice_height);
+ uniform_num_samples = src_bilinear_samples;
+ uniform_num_loops = num_loops;
+ uniform_slice_height = slice_height;
// Instructions for how to convert integer sample numbers to positions in the weight texture.
- set_uniform_float(glsl_program_num, prefix, "sample_x_scale", 1.0f / src_bilinear_samples);
- set_uniform_float(glsl_program_num, prefix, "sample_x_offset", 0.5f / src_bilinear_samples);
+ uniform_sample_x_scale = 1.0f / src_bilinear_samples;
+ uniform_sample_x_offset = 0.5f / src_bilinear_samples;
- float whole_pixel_offset;
if (direction == SingleResamplePassEffect::VERTICAL) {
- whole_pixel_offset = lrintf(offset) / float(input_height);
+ uniform_whole_pixel_offset = lrintf(offset) / float(input_height);
} else {
- whole_pixel_offset = lrintf(offset) / float(input_width);
+ uniform_whole_pixel_offset = lrintf(offset) / float(input_width);
}
- set_uniform_float(glsl_program_num, prefix, "whole_pixel_offset", whole_pixel_offset);
// We specifically do not want mipmaps on the input texture;
// they break minification.
Node *self = chain->find_node_for_effect(this);
- glActiveTexture(chain->get_input_sampler(self, 0));
- check_error();
- glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
- check_error();
+ if (chain->has_input_sampler(self, 0)) {
+ glActiveTexture(chain->get_input_sampler(self, 0));
+ check_error();
+ glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
+ check_error();
+ }
}
} // namespace movit
projects / movit / blobdiff