X-Git-Url: https://git.sesse.net/?p=movit;a=blobdiff_plain;f=resample_effect.cpp;h=9c8caf3bb77ed58bf2d143dcc2b3b837b81a001c;hp=20c2f9b24c60f6bcf086f3665a771fac4012c8c2;hb=2fd06b9c44225d1e740cb2de08a9dfa5c9cd0031;hpb=3789397e29df3bade367c8963b050d8add510c0f diff --git a/resample_effect.cpp b/resample_effect.cpp index 20c2f9b..9c8caf3 100644 --- a/resample_effect.cpp +++ b/resample_effect.cpp @@ -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 @@ -7,13 +9,18 @@ #include #include #include +#include +#include +#include #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 *src, Tap *dst, unsigned num_src_samples, unsigned max_samples_saved) +template +unsigned combine_samples(const Tap *src, Tap *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(src[i].weight); + dst[j].pos = convert_float(src[i].pos); } if (i == num_src_samples - 1) { @@ -85,22 +161,23 @@ unsigned combine_samples(Tap *src, Tap *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 *src, Tap *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 +void normalize_sum(Tap* 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(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 +unsigned combine_many_samples(const Tap *weights, unsigned src_size, unsigned src_samples, unsigned dst_samples, Tap **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(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[dst_samples * src_bilinear_samples]; + for (unsigned y = 0; y < dst_samples; ++y) { + Tap *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 . 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 +double compute_sum_sq_error(const Tap* weights, unsigned num_weights, + const Tap* 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(lower_pos, lrintf(weights[0].pos * size - 0.5)); + upper_pos = max(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 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(src_bilinear_samples, src_samples - num_samples_saved); - } - - // Now that we know the right width, actually combine the samples. - Tap *bilinear_weights = new Tap[dst_samples * src_bilinear_samples]; - Tap *bilinear_weights_fp16 = new Tap[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 *bilinear_weights_fp16; + src_bilinear_samples = combine_many_samples(weights, src_size, src_samples, dst_samples, &bilinear_weights_fp16); + Tap *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 *bilinear_weights_ptr = bilinear_weights + y * src_bilinear_samples; - Tap *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