X-Git-Url: https://git.sesse.net/?p=movit;a=blobdiff_plain;f=resample_effect.cpp;h=5ea5fe4bd91f80f1d260c52baaeebbb63dabd7b7;hp=3ccb2fdc4054894ad49e15f2f7035033ddb6adbd;hb=833bbfaf5387f213e6a9c355b93aa622c74ec88f;hpb=42f0fd5ccbb3560a76d55f3e725416a5e0f93523 diff --git a/resample_effect.cpp b/resample_effect.cpp index 3ccb2fd..5ea5fe4 100644 --- a/resample_effect.cpp +++ b/resample_effect.cpp @@ -7,13 +7,18 @@ #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 { @@ -55,13 +60,15 @@ unsigned gcd(unsigned a, unsigned b) return a; } -unsigned combine_samples(Tap *src, Tap *dst, unsigned src_size, unsigned num_src_samples, unsigned max_samples_saved) +template +unsigned combine_samples(const Tap *src, Tap *dst, unsigned src_size, unsigned num_src_samples, unsigned max_samples_saved) { unsigned num_samples_saved = 0; 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) { @@ -85,15 +92,16 @@ unsigned combine_samples(Tap *src, Tap *dst, unsigned src_size, un float pos2 = src[i + 1].pos; assert(pos2 > pos1); - float pos, total_weight, sum_sq_error; - combine_two_samples(w1, w2, pos1, pos2, src_size, COMBINE_ROUND_TO_FP16, &pos, &total_weight, &sum_sq_error); + fp16_int_t pos, total_weight; + float sum_sq_error; + combine_two_samples(w1, w2, pos1, pos2, src_size, &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; } @@ -109,6 +117,219 @@ unsigned combine_samples(Tap *src, Tap *dst, unsigned src_size, un 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) { + double sum = 0.0; + for (unsigned i = 0; i < num; ++i) { + sum += to_fp64(vals[i].weight); + } + for (unsigned i = 0; i < num; ++i) { + vals[i].weight = from_fp64(to_fp64(vals[i].weight) / 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) +{ + int src_bilinear_samples = 0; + for (unsigned y = 0; y < dst_samples; ++y) { + unsigned num_samples_saved = combine_samples(weights + y * src_samples, NULL, src_size, 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. + *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, + src_size, + src_samples, + src_samples - src_bilinear_samples); + assert(int(src_samples) - int(num_samples_saved) == src_bilinear_samples); + 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_fp64(bilinear_weights[0].pos) * size - 0.5)); + int upper_pos = int(ceil(to_fp64(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)); + + 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_fp64(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_fp64(bilinear_weights[i].weight) * (1.0 - f); + effective_weights[x1] += to_fp64(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; +} + +// Given a predefined, fixed set of bilinear weight positions, try to optimize +// their weights through some linear algebra. This can do a better job than +// the weight calculation in combine_samples() because it can look at the entire +// picture (an effective weight can sometimes be affected by multiple samples). +// It will also optimize weights for non-combined samples, which is useful when +// a sample happens in-between texels for numerical reasons. +// +// The math goes as follows: The desired result is a weighted sum, where the +// weights are the coefficients in : +// +// y = sum(c_j x_j, j) +// +// We try to approximate this by a different set of coefficients, which have +// weights d_i and are placed at some fraction to the right of a source texel x_j. +// This means it will influence two texels (x_j and x_{j+1}); generalizing this, +// let us define that w_ij means the amount texel influences bilinear weight +// (keeping in mind that w_ij = 0 for all but at most two different j). +// This means the actually computed result is: +// +// y' = sum(d_i w_ij x_j, j) +// +// We assume w_ij fixed and wish to find {d_i} so that y' gets as close to y +// as possible. Specifically, let us consider the sum of squred errors of the +// coefficients: +// +// ε² = sum((sum( d_i w_ij, i ) - c_j)², j) +// +// The standard trick, which also applies just fine here, is to differentiate +// the error with respect to each variable we wish to optimize, and set each +// such expression to zero. Solving this equation set (which we can do efficiently +// by letting Eigen invert a sparse matrix for us) yields the minimum possible +// error. To see the form each such equation takes, pick any value k and +// differentiate the expression by d_k: +// +// ∂(ε²)/∂(d_k) = sum(2(sum( d_i w_ij, i ) - c_j) w_kj, j) +// +// Setting this expression equal to zero, dropping the irrelevant factor 2 and +// rearranging yields: +// +// sum(w_kj sum( d_i w_ij, i ), j) = sum(w_kj c_j, j) +// +// where again, we remember where the sums over j are over at most two elements, +// since w_ij is nonzero for at most two values of j. +template +void optimize_sum_sq_error(const Tap* weights, unsigned num_weights, + Tap* bilinear_weights, unsigned num_bilinear_weights, + unsigned size) +{ + // Find the range of the desired weights. + int c_lower_pos = lrintf(weights[0].pos * size - 0.5); + int c_upper_pos = lrintf(weights[num_weights - 1].pos * size - 0.5) + 1; + + SparseMatrix A(num_bilinear_weights, num_bilinear_weights); + SparseVector b(num_bilinear_weights); + + // Convert each bilinear weight to the (x, frac) form for less junk in the code below. + int* pos = new int[num_bilinear_weights]; + float* fracs = new float[num_bilinear_weights]; + for (unsigned i = 0; i < num_bilinear_weights; ++i) { + const float pixel_pos = to_fp64(bilinear_weights[i].pos) * size - 0.5f; + const float f = pixel_pos - floor(pixel_pos); + pos[i] = int(floor(pixel_pos)); + fracs[i] = lrintf(f / movit_texel_subpixel_precision) * movit_texel_subpixel_precision; + } + + // The index ordering is a bit unusual to fit better with the + // notation in the derivation above. + for (unsigned k = 0; k < num_bilinear_weights; ++k) { + for (int j = pos[k]; j <= pos[k] + 1; ++j) { + const float f_kj = (j == pos[k]) ? (1.0f - fracs[k]) : fracs[k]; + for (unsigned i = 0; i < num_bilinear_weights; ++i) { + float f_ij; + if (j == pos[i]) { + f_ij = 1.0f - fracs[i]; + } else if (j == pos[i] + 1) { + f_ij = fracs[i]; + } else { + // f_ij = 0 + continue; + } + A.coeffRef(i, k) += f_kj * f_ij; + } + float c_j; + if (j >= c_lower_pos && j < c_upper_pos) { + c_j = weights[j - c_lower_pos].weight; + } else { + c_j = 0.0f; + } + b.coeffRef(k) += f_kj * c_j; + } + } + delete[] pos; + delete[] fracs; + + A.makeCompressed(); + SparseQR, COLAMDOrdering > qr(A); + assert(qr.info() == Success); + SparseMatrix new_weights = qr.solve(b); + assert(qr.info() == Success); + + for (unsigned i = 0; i < num_bilinear_weights; ++i) { + bilinear_weights[i].weight = from_fp64(new_weights.coeff(i, 0)); + } + normalize_sum(bilinear_weights, num_bilinear_weights); +} + } // namespace ResampleEffect::ResampleEffect() @@ -394,50 +615,34 @@ void SingleResamplePassEffect::update_texture(GLuint glsl_program_num, const str } // 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. + 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) { - unsigned num_samples_saved = combine_samples(weights + y * src_samples, NULL, src_size, src_samples, UINT_MAX); - src_bilinear_samples = max(src_bilinear_samples, src_samples - num_samples_saved); + optimize_sum_sq_error( + weights + y * src_samples, src_samples, + bilinear_weights_fp16 + y * src_bilinear_samples, src_bilinear_samples, + src_size); + 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); } - // 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]; - 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_size, - 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); - } - - // 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); - } + // 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. + if (max_sum_sq_error_fp16 > 2.0f / (255.0f * 255.0f)) { + fallback_to_fp32 = true; + src_bilinear_samples = combine_many_samples(weights, src_size, src_samples, dst_samples, &bilinear_weights_fp32); + for (unsigned y = 0; y < dst_samples; ++y) { + optimize_sum_sq_error( + weights + y * src_samples, src_samples, + bilinear_weights_fp32 + y * src_bilinear_samples, src_bilinear_samples, + src_size); } } @@ -452,12 +657,16 @@ void SingleResamplePassEffect::update_texture(GLuint glsl_program_num, const str 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 (fallback_to_fp32) { + glTexImage2D(GL_TEXTURE_2D, 0, GL_RG32F, src_bilinear_samples, dst_samples, 0, GL_RG, GL_FLOAT, bilinear_weights_fp32); + } else { + glTexImage2D(GL_TEXTURE_2D, 0, GL_RG16F, src_bilinear_samples, dst_samples, 0, GL_RG, GL_HALF_FLOAT, bilinear_weights_fp16); + } 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)