Optimize VAO/VBO usage for minimal state changes.
[movit] / resample_effect.cpp
index 20c2f9b..9c8caf3 100644 (file)
@@ -1,4 +1,6 @@
 // Three-lobed Lanczos, the most common choice.
+// Note that if you change this, the accuracy for LANCZOS_TABLE_SIZE
+// needs to be recomputed.
 #define LANCZOS_RADIUS 3.0
 
 #include <epoxy/gl.h>
@@ -7,13 +9,18 @@
 #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 {
@@ -35,15 +42,67 @@ float sinc(float x)
        }
 }
 
-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);
+       int 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.
 unsigned gcd(unsigned a, unsigned b)
 {
@@ -55,13 +114,30 @@ unsigned gcd(unsigned a, unsigned b)
        return a;
 }
 
-unsigned combine_samples(Tap<float> *src, Tap<float> *dst, unsigned num_src_samples, unsigned max_samples_saved)
+template<class DestFloat>
+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) {
-                       dst[j] = src[i];
+                       dst[j].weight = convert_float<float, DestFloat>(src[i].weight);
+                       dst[j].pos = convert_float<float, DestFloat>(src[i].pos);
                }
 
                if (i == num_src_samples - 1) {
@@ -85,22 +161,23 @@ unsigned combine_samples(Tap<float> *src, Tap<float> *dst, unsigned num_src_samp
                float pos2 = src[i + 1].pos;
                assert(pos2 > pos1);
 
-               float offset, total_weight, sum_sq_error;
-               combine_two_samples(w1, w2, &offset, &total_weight, &sum_sq_error);
+               DestFloat pos, total_weight;
+               float 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;
                }
 
                // OK, we can combine this and the next sample.
                if (dst != NULL) {
                        dst[j].weight = total_weight;
-                       dst[j].pos = pos1 + offset * (pos2 - pos1);
+                       dst[j].pos = pos;
                }
 
                ++i;  // Skip the next sample.
@@ -109,6 +186,119 @@ unsigned combine_samples(Tap<float> *src, Tap<float> *dst, unsigned num_src_samp
        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, 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 = new Tap<DestFloat>[dst_samples * src_bilinear_samples];
+       for (unsigned y = 0; y < dst_samples; ++y) {
+               Tap<DestFloat> *bilinear_weights_ptr = *bilinear_weights + 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 - 0.5));
+       int upper_pos = int(ceil(to_fp32(bilinear_weights[num_bilinear_weights - 1].pos) * size - 0.5)) + 2;
+       lower_pos = min<int>(lower_pos, lrintf(weights[0].pos * size - 0.5));
+       upper_pos = max<int>(upper_pos, lrintf(weights[num_weights - 1].pos * size - 0.5) + 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) * (1.0 - 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()
@@ -250,7 +440,8 @@ SingleResamplePassEffect::SingleResamplePassEffect(ResampleEffect *parent)
          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);
@@ -259,8 +450,21 @@ SingleResamplePassEffect::SingleResamplePassEffect(ResampleEffect *parent)
        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()
@@ -387,57 +591,36 @@ void SingleResamplePassEffect::update_texture(GLuint glsl_program_num, const str
                // Now sample <int_radius> pixels on each side around that point.
                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);
                }
        }
 
        // 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;
-       for (unsigned y = 0; y < dst_samples; ++y) {
-               unsigned num_samples_saved = combine_samples(weights + y * src_samples, NULL, 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<float> *bilinear_weights = new Tap<float>[dst_samples * src_bilinear_samples];
-       Tap<fp16_int_t> *bilinear_weights_fp16 = new Tap<fp16_int_t>[dst_samples * src_bilinear_samples];
+       // 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);
+       Tap<fp16_int_t> *bilinear_weights_fp16;
+       src_bilinear_samples = combine_many_samples(weights, src_size, src_samples, dst_samples, &bilinear_weights_fp16);
+       Tap<float> *bilinear_weights_fp32 = NULL;
+       bool fallback_to_fp32 = false;
+       double max_sum_sq_error_fp16 = 0.0;
        for (unsigned y = 0; y < dst_samples; ++y) {
-               Tap<float> *bilinear_weights_ptr = bilinear_weights + y * src_bilinear_samples;
-               Tap<fp16_int_t> *bilinear_weights_fp16_ptr = bilinear_weights_fp16 + y * src_bilinear_samples;
-               unsigned num_samples_saved = combine_samples(
-                       weights + y * src_samples,
-                       bilinear_weights_ptr,
-                       src_samples,
-                       src_samples - src_bilinear_samples);
-               assert(int(src_samples) - int(num_samples_saved) == src_bilinear_samples);
-
-               // Convert to fp16.
-               for (int i = 0; i < src_bilinear_samples; ++i) {
-                       bilinear_weights_fp16_ptr[i].weight = fp64_to_fp16(bilinear_weights_ptr[i].weight);
-                       bilinear_weights_fp16_ptr[i].pos    = fp64_to_fp16(bilinear_weights_ptr[i].pos);
+               double sum_sq_error_fp16 = compute_sum_sq_error(
+                       weights + y * src_samples, src_samples,
+                       bilinear_weights_fp16 + 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;
                }
+       }
 
-               // 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_fp16_ptr[i].weight);
-                       }
-                       for (int i = 0; i < src_bilinear_samples; ++i) {
-                               bilinear_weights_fp16_ptr[i].weight = fp64_to_fp16(
-                                       fp16_to_fp64(bilinear_weights_fp16_ptr[i].weight) / sum);
-                       }
-               }
+       if (max_sum_sq_error_fp16 > max_error) {
+               fallback_to_fp32 = true;
+               src_bilinear_samples = combine_many_samples(weights, src_size, src_samples, dst_samples, &bilinear_weights_fp32);
        }
 
        // Encode as a two-component texture. Note the GL_REPEAT.
@@ -445,18 +628,45 @@ void SingleResamplePassEffect::update_texture(GLuint glsl_program_num, const str
        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_fp16);
+       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;
+       if (fallback_to_fp32) {
+               type = GL_FLOAT;
+               internal_format = GL_RG32F;
+               pixels = bilinear_weights_fp32;
+       } else {
+               type = GL_HALF_FLOAT;
+               internal_format = GL_RG16F;
+               pixels = bilinear_weights_fp16;
+       }
+
+       if (int(src_bilinear_samples) == last_texture_width &&
+           int(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, src_bilinear_samples, dst_samples, GL_RG, type, pixels);
+       } else {
+               glTexImage2D(GL_TEXTURE_2D, 0, internal_format, src_bilinear_samples, dst_samples, 0, GL_RG, type, pixels);
+               last_texture_width = src_bilinear_samples;
+               last_texture_height = dst_samples;
+               last_texture_internal_format = internal_format;
+       }
        check_error();
 
        delete[] weights;
-       delete[] bilinear_weights;
        delete[] bilinear_weights_fp16;
+       delete[] bilinear_weights_fp32;
 }
 
 void SingleResamplePassEffect::set_gl_state(GLuint glsl_program_num, const string &prefix, unsigned *sampler_num)
@@ -488,31 +698,31 @@ void SingleResamplePassEffect::set_gl_state(GLuint glsl_program_num, const strin
        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