1 // Three-lobed Lanczos, the most common choice.
2 // Note that if you change this, the accuracy for LANCZOS_TABLE_SIZE
3 // needs to be recomputed.
4 #define LANCZOS_RADIUS 3.0
12 #include <Eigen/Sparse>
13 #include <Eigen/SparseQR>
14 #include <Eigen/OrderingMethods>
16 #include "effect_chain.h"
17 #include "effect_util.h"
20 #include "resample_effect.h"
23 using namespace Eigen;
39 return 1.0f - fabs(x);
45 float lanczos_weight(float x)
47 if (fabs(x) > LANCZOS_RADIUS) {
50 return sinc(M_PI * x) * sinc((M_PI / LANCZOS_RADIUS) * x);
54 // The weight function can be expensive to compute over and over again
55 // (which will happen during e.g. a zoom), but it is also easy to interpolate
56 // linearly. We compute the right half of the function (in the range of
57 // 0..LANCZOS_RADIUS), with two guard elements for easier interpolation, and
58 // linearly interpolate to get our function.
60 // We want to scale the table so that the maximum error is always smaller
61 // than 1e-6. As per http://www-solar.mcs.st-andrews.ac.uk/~clare/Lectures/num-analysis/Numan_chap3.pdf,
62 // the error for interpolating a function linearly between points [a,b] is
64 // e = 1/2 (x-a)(x-b) f''(u_x)
66 // for some point u_x in [a,b] (where f(x) is our Lanczos function; we're
67 // assuming LANCZOS_RADIUS=3 from here on). Obviously this is bounded by
68 // f''(x) over the entire range. Numeric optimization shows the maximum of
69 // |f''(x)| to be in x=1.09369819474562880, with the value 2.40067758733152381.
70 // So if the steps between consecutive values are called d, we get
72 // |e| <= 1/2 (d/2)^2 2.4007
75 // Solve for e = 1e-6 yields a step size of 0.0027, which to cover the range
76 // 0..3 needs 1109 steps. We round up to the next power of two, just to be sure.
77 #define LANCZOS_TABLE_SIZE 2048
78 bool lanczos_table_init_done = false;
79 float lanczos_table[LANCZOS_TABLE_SIZE + 2];
81 void init_lanczos_table()
83 for (unsigned i = 0; i < LANCZOS_TABLE_SIZE + 2; ++i) {
84 lanczos_table[i] = lanczos_weight(float(i) * (LANCZOS_RADIUS / LANCZOS_TABLE_SIZE));
86 lanczos_table_init_done = true;
89 float lanczos_weight_cached(float x)
91 if (!lanczos_table_init_done) {
92 // Could in theory race between two threads if we are unlucky,
93 // but that is harmless, since they'll write the same data.
97 if (x > LANCZOS_RADIUS) {
100 float table_pos = x * (LANCZOS_TABLE_SIZE / LANCZOS_RADIUS);
101 int table_pos_int = int(table_pos); // Truncate towards zero.
102 float table_pos_frac = table_pos - table_pos_int;
103 assert(table_pos < LANCZOS_TABLE_SIZE + 2);
104 return lanczos_table[table_pos_int] +
105 table_pos_frac * (lanczos_table[table_pos_int + 1] - lanczos_table[table_pos_int]);
108 // Euclid's algorithm, from Wikipedia.
109 unsigned gcd(unsigned a, unsigned b)
119 template<class DestFloat>
120 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)
122 // Cut off near-zero values at both sides.
123 unsigned num_samples_saved = 0;
124 while (num_samples_saved < max_samples_saved &&
125 num_src_samples > 0 &&
126 fabs(src[0].weight) < 1e-6) {
131 while (num_samples_saved < max_samples_saved &&
132 num_src_samples > 0 &&
133 fabs(src[num_src_samples - 1].weight) < 1e-6) {
138 for (unsigned i = 0, j = 0; i < num_src_samples; ++i, ++j) {
139 // Copy the sample directly; it will be overwritten later if we can combine.
141 dst[j].weight = convert_float<float, DestFloat>(src[i].weight);
142 dst[j].pos = convert_float<float, DestFloat>(src[i].pos);
145 if (i == num_src_samples - 1) {
146 // Last sample; cannot combine.
149 assert(num_samples_saved <= max_samples_saved);
150 if (num_samples_saved == max_samples_saved) {
151 // We could maybe save more here, but other rows can't, so don't bother.
155 float w1 = src[i].weight;
156 float w2 = src[i + 1].weight;
157 if (w1 * w2 < 0.0f) {
158 // Differing signs; cannot combine.
162 float pos1 = src[i].pos;
163 float pos2 = src[i + 1].pos;
166 DestFloat pos, total_weight;
168 combine_two_samples(w1, w2, pos1, pos2, num_subtexels, inv_num_subtexels, &pos, &total_weight, &sum_sq_error);
170 // If the interpolation error is larger than that of about sqrt(2) of
171 // a level at 8-bit precision, don't combine. (You'd think 1.0 was enough,
172 // but since the artifacts are not really random, they can get quite
173 // visible. On the other hand, going to 0.25f, I can see no change at
174 // all with 8-bit output, so it would not seem to be worth it.)
175 if (sum_sq_error > 0.5f / (255.0f * 255.0f)) {
179 // OK, we can combine this and the next sample.
181 dst[j].weight = total_weight;
185 ++i; // Skip the next sample.
188 return num_samples_saved;
191 // Normalize so that the sum becomes one. Note that we do it twice;
192 // this sometimes helps a tiny little bit when we have many samples.
194 void normalize_sum(Tap<T>* vals, unsigned num)
196 for (int normalize_pass = 0; normalize_pass < 2; ++normalize_pass) {
198 for (unsigned i = 0; i < num; ++i) {
199 sum += to_fp64(vals[i].weight);
201 double inv_sum = 1.0 / sum;
202 for (unsigned i = 0; i < num; ++i) {
203 vals[i].weight = from_fp64<T>(to_fp64(vals[i].weight) * inv_sum);
208 // Make use of the bilinear filtering in the GPU to reduce the number of samples
209 // we need to make. This is a bit more complex than BlurEffect since we cannot combine
210 // two neighboring samples if their weights have differing signs, so we first need to
211 // figure out the maximum number of samples. Then, we downconvert all the weights to
212 // that number -- we could have gone for a variable-length system, but this is simpler,
213 // and the gains would probably be offset by the extra cost of checking when to stop.
215 // The greedy strategy for combining samples is optimal.
216 template<class DestFloat>
217 unsigned combine_many_samples(const Tap<float> *weights, unsigned src_size, unsigned src_samples, unsigned dst_samples, Tap<DestFloat> **bilinear_weights)
219 float num_subtexels = src_size / movit_texel_subpixel_precision;
220 float inv_num_subtexels = movit_texel_subpixel_precision / src_size;
222 unsigned max_samples_saved = UINT_MAX;
223 for (unsigned y = 0; y < dst_samples && max_samples_saved > 0; ++y) {
224 unsigned num_samples_saved = combine_samples<DestFloat>(weights + y * src_samples, NULL, num_subtexels, inv_num_subtexels, src_samples, max_samples_saved);
225 max_samples_saved = min(max_samples_saved, num_samples_saved);
228 // Now that we know the right width, actually combine the samples.
229 unsigned src_bilinear_samples = src_samples - max_samples_saved;
230 *bilinear_weights = new Tap<DestFloat>[dst_samples * src_bilinear_samples];
231 for (unsigned y = 0; y < dst_samples; ++y) {
232 Tap<DestFloat> *bilinear_weights_ptr = *bilinear_weights + y * src_bilinear_samples;
233 unsigned num_samples_saved = combine_samples(
234 weights + y * src_samples,
235 bilinear_weights_ptr,
240 assert(num_samples_saved == max_samples_saved);
241 normalize_sum(bilinear_weights_ptr, src_bilinear_samples);
243 return src_bilinear_samples;
246 // Compute the sum of squared errors between the ideal weights (which are
247 // assumed to fall exactly on pixel centers) and the weights that result
248 // from sampling at <bilinear_weights>. The primary reason for the difference
249 // is inaccuracy in the sampling positions, both due to limited precision
250 // in storing them (already inherent in sending them in as fp16_int_t)
251 // and in subtexel sampling precision (which we calculate in this function).
253 double compute_sum_sq_error(const Tap<float>* weights, unsigned num_weights,
254 const Tap<T>* bilinear_weights, unsigned num_bilinear_weights,
257 // Find the effective range of the bilinear-optimized kernel.
258 // Due to rounding of the positions, this is not necessarily the same
259 // as the intended range (ie., the range of the original weights).
260 int lower_pos = int(floor(to_fp64(bilinear_weights[0].pos) * size - 0.5));
261 int upper_pos = int(ceil(to_fp64(bilinear_weights[num_bilinear_weights - 1].pos) * size - 0.5)) + 2;
262 lower_pos = min<int>(lower_pos, lrintf(weights[0].pos * size - 0.5));
263 upper_pos = max<int>(upper_pos, lrintf(weights[num_weights - 1].pos * size - 0.5) + 1);
265 float* effective_weights = new float[upper_pos - lower_pos];
266 for (int i = 0; i < upper_pos - lower_pos; ++i) {
267 effective_weights[i] = 0.0f;
270 // Now find the effective weights that result from this sampling.
271 for (unsigned i = 0; i < num_bilinear_weights; ++i) {
272 const float pixel_pos = to_fp64(bilinear_weights[i].pos) * size - 0.5f;
273 const int x0 = int(floor(pixel_pos)) - lower_pos;
274 const int x1 = x0 + 1;
275 const float f = lrintf((pixel_pos - (x0 + lower_pos)) / movit_texel_subpixel_precision) * movit_texel_subpixel_precision;
279 assert(x0 < upper_pos - lower_pos);
280 assert(x1 < upper_pos - lower_pos);
282 effective_weights[x0] += to_fp64(bilinear_weights[i].weight) * (1.0 - f);
283 effective_weights[x1] += to_fp64(bilinear_weights[i].weight) * f;
286 // Subtract the desired weights to get the error.
287 for (unsigned i = 0; i < num_weights; ++i) {
288 const int x = lrintf(weights[i].pos * size - 0.5f) - lower_pos;
290 assert(x < upper_pos - lower_pos);
292 effective_weights[x] -= weights[i].weight;
295 double sum_sq_error = 0.0;
296 for (unsigned i = 0; i < num_weights; ++i) {
297 sum_sq_error += effective_weights[i] * effective_weights[i];
300 delete[] effective_weights;
306 ResampleEffect::ResampleEffect()
309 offset_x(0.0f), offset_y(0.0f),
310 zoom_x(1.0f), zoom_y(1.0f),
311 zoom_center_x(0.5f), zoom_center_y(0.5f)
313 register_int("width", &output_width);
314 register_int("height", &output_height);
316 // The first blur pass will forward resolution information to us.
317 hpass = new SingleResamplePassEffect(this);
318 CHECK(hpass->set_int("direction", SingleResamplePassEffect::HORIZONTAL));
319 vpass = new SingleResamplePassEffect(NULL);
320 CHECK(vpass->set_int("direction", SingleResamplePassEffect::VERTICAL));
325 void ResampleEffect::rewrite_graph(EffectChain *graph, Node *self)
327 Node *hpass_node = graph->add_node(hpass);
328 Node *vpass_node = graph->add_node(vpass);
329 graph->connect_nodes(hpass_node, vpass_node);
330 graph->replace_receiver(self, hpass_node);
331 graph->replace_sender(self, vpass_node);
332 self->disabled = true;
335 // We get this information forwarded from the first blur pass,
336 // since we are not part of the chain ourselves.
337 void ResampleEffect::inform_input_size(unsigned input_num, unsigned width, unsigned height)
339 assert(input_num == 0);
343 input_height = height;
347 void ResampleEffect::update_size()
350 ok |= hpass->set_int("input_width", input_width);
351 ok |= hpass->set_int("input_height", input_height);
352 ok |= hpass->set_int("output_width", output_width);
353 ok |= hpass->set_int("output_height", input_height);
355 ok |= vpass->set_int("input_width", output_width);
356 ok |= vpass->set_int("input_height", input_height);
357 ok |= vpass->set_int("output_width", output_width);
358 ok |= vpass->set_int("output_height", output_height);
362 // The offset added due to zoom may have changed with the size.
363 update_offset_and_zoom();
366 void ResampleEffect::update_offset_and_zoom()
370 // Zoom from the right origin. (zoom_center is given in normalized coordinates,
372 float extra_offset_x = zoom_center_x * (1.0f - 1.0f / zoom_x) * input_width;
373 float extra_offset_y = (1.0f - zoom_center_y) * (1.0f - 1.0f / zoom_y) * input_height;
375 ok |= hpass->set_float("offset", extra_offset_x + offset_x);
376 ok |= vpass->set_float("offset", extra_offset_y - offset_y); // Compensate for the bottom-left origin.
377 ok |= hpass->set_float("zoom", zoom_x);
378 ok |= vpass->set_float("zoom", zoom_y);
383 bool ResampleEffect::set_float(const string &key, float value) {
384 if (key == "width") {
385 output_width = value;
389 if (key == "height") {
390 output_height = value;
396 update_offset_and_zoom();
401 update_offset_and_zoom();
404 if (key == "zoom_x") {
409 update_offset_and_zoom();
412 if (key == "zoom_y") {
417 update_offset_and_zoom();
420 if (key == "zoom_center_x") {
421 zoom_center_x = value;
422 update_offset_and_zoom();
425 if (key == "zoom_center_y") {
426 zoom_center_y = value;
427 update_offset_and_zoom();
433 SingleResamplePassEffect::SingleResamplePassEffect(ResampleEffect *parent)
435 direction(HORIZONTAL),
440 last_input_width(-1),
441 last_input_height(-1),
442 last_output_width(-1),
443 last_output_height(-1),
444 last_offset(0.0 / 0.0), // NaN.
445 last_zoom(0.0 / 0.0), // NaN.
446 last_texture_width(-1), last_texture_height(-1)
448 register_int("direction", (int *)&direction);
449 register_int("input_width", &input_width);
450 register_int("input_height", &input_height);
451 register_int("output_width", &output_width);
452 register_int("output_height", &output_height);
453 register_float("offset", &offset);
454 register_float("zoom", &zoom);
455 register_uniform_sampler2d("sample_tex", &uniform_sample_tex);
456 register_uniform_int("num_samples", &uniform_num_samples); // FIXME: What about GLSL pre-1.30?
457 register_uniform_float("num_loops", &uniform_num_loops);
458 register_uniform_float("slice_height", &uniform_slice_height);
459 register_uniform_float("sample_x_scale", &uniform_sample_x_scale);
460 register_uniform_float("sample_x_offset", &uniform_sample_x_offset);
461 register_uniform_float("whole_pixel_offset", &uniform_whole_pixel_offset);
463 glGenTextures(1, &texnum);
466 SingleResamplePassEffect::~SingleResamplePassEffect()
468 glDeleteTextures(1, &texnum);
471 string SingleResamplePassEffect::output_fragment_shader()
474 sprintf(buf, "#define DIRECTION_VERTICAL %d\n", (direction == VERTICAL));
475 return buf + read_file("resample_effect.frag");
478 // Using vertical scaling as an example:
480 // Generally out[y] = w0 * in[yi] + w1 * in[yi + 1] + w2 * in[yi + 2] + ...
482 // Obviously, yi will depend on y (in a not-quite-linear way), but so will
483 // the weights w0, w1, w2, etc.. The easiest way of doing this is to encode,
484 // for each sample, the weight and the yi value, e.g. <yi, w0>, <yi + 1, w1>,
485 // and so on. For each y, we encode these along the x-axis (since that is spare),
486 // so out[0] will read from parameters <x,y> = <0,0>, <1,0>, <2,0> and so on.
488 // For horizontal scaling, we fill in the exact same texture;
489 // the shader just interprets it differently.
490 void SingleResamplePassEffect::update_texture(GLuint glsl_program_num, const string &prefix, unsigned *sampler_num)
492 unsigned src_size, dst_size;
493 if (direction == SingleResamplePassEffect::HORIZONTAL) {
494 assert(input_height == output_height);
495 src_size = input_width;
496 dst_size = output_width;
497 } else if (direction == SingleResamplePassEffect::VERTICAL) {
498 assert(input_width == output_width);
499 src_size = input_height;
500 dst_size = output_height;
505 // For many resamplings (e.g. 640 -> 1280), we will end up with the same
506 // set of samples over and over again in a loop. Thus, we can compute only
507 // the first such loop, and then ask the card to repeat the texture for us.
508 // This is both easier on the texture cache and lowers our CPU cost for
509 // generating the kernel somewhat.
510 float scaling_factor;
511 if (fabs(zoom - 1.0f) < 1e-6) {
512 num_loops = gcd(src_size, dst_size);
513 scaling_factor = float(dst_size) / float(src_size);
515 // If zooming is enabled (ie., zoom != 1), we turn off the looping.
516 // We _could_ perhaps do it for rational zoom levels (especially
517 // things like 2:1), but it doesn't seem to be worth it, given that
518 // the most common use case would seem to be varying the zoom
519 // from frame to frame.
521 scaling_factor = zoom * float(dst_size) / float(src_size);
523 slice_height = 1.0f / num_loops;
524 unsigned dst_samples = dst_size / num_loops;
526 // Sample the kernel in the right place. A diagram with a triangular kernel
527 // (corresponding to linear filtering, and obviously with radius 1)
528 // for easier ASCII art drawing:
534 // x---x---x x x---x---x---x
536 // Scaling up (in this case, 2x) means sampling more densely:
542 // x-x-x-x-x-x x x x-x-x-x-x-x-x-x
544 // When scaling up, any destination pixel will only be influenced by a few
545 // (in this case, two) neighboring pixels, and more importantly, the number
546 // will not be influenced by the scaling factor. (Note, however, that the
547 // pixel centers have moved, due to OpenGL's center-pixel convention.)
548 // The only thing that changes is the weights themselves, as the sampling
549 // points are at different distances from the original pixels.
551 // Scaling down is a different story:
557 // --x------ x --x-------x--
559 // Again, the pixel centers have moved in a maybe unintuitive fashion,
560 // although when you consider that there are multiple source pixels around,
561 // it's not so bad as at first look:
567 // --x-------x-------x-------x--
569 // As you can see, the new pixels become averages of the two neighboring old
570 // ones (the situation for Lanczos is of course more complex).
572 // Anyhow, in this case we clearly need to look at more source pixels
573 // to compute the destination pixel, and how many depend on the scaling factor.
574 // Thus, the kernel width will vary with how much we scale.
575 float radius_scaling_factor = min(scaling_factor, 1.0f);
576 int int_radius = lrintf(LANCZOS_RADIUS / radius_scaling_factor);
577 int src_samples = int_radius * 2 + 1;
578 Tap<float> *weights = new Tap<float>[dst_samples * src_samples];
579 float subpixel_offset = offset - lrintf(offset); // The part not covered by whole_pixel_offset.
580 assert(subpixel_offset >= -0.5f && subpixel_offset <= 0.5f);
581 for (unsigned y = 0; y < dst_samples; ++y) {
582 // Find the point around which we want to sample the source image,
583 // compensating for differing pixel centers as the scale changes.
584 float center_src_y = (y + 0.5f) / scaling_factor - 0.5f;
585 int base_src_y = lrintf(center_src_y);
587 // Now sample <int_radius> pixels on each side around that point.
588 for (int i = 0; i < src_samples; ++i) {
589 int src_y = base_src_y + i - int_radius;
590 float weight = lanczos_weight_cached(radius_scaling_factor * (src_y - center_src_y - subpixel_offset));
591 weights[y * src_samples + i].weight = weight * radius_scaling_factor;
592 weights[y * src_samples + i].pos = (src_y + 0.5) / float(src_size);
596 // Now make use of the bilinear filtering in the GPU to reduce the number of samples
597 // we need to make. Try fp16 first; if it's not accurate enough, we go to fp32.
598 // Our tolerance level for total error is a bit higher than the one for invididual
599 // samples, since one would assume overall errors in the shape don't matter as much.
600 const float max_error = 2.0f / (255.0f * 255.0f);
601 Tap<fp16_int_t> *bilinear_weights_fp16;
602 src_bilinear_samples = combine_many_samples(weights, src_size, src_samples, dst_samples, &bilinear_weights_fp16);
603 Tap<float> *bilinear_weights_fp32 = NULL;
604 bool fallback_to_fp32 = false;
605 double max_sum_sq_error_fp16 = 0.0;
606 for (unsigned y = 0; y < dst_samples; ++y) {
607 double sum_sq_error_fp16 = compute_sum_sq_error(
608 weights + y * src_samples, src_samples,
609 bilinear_weights_fp16 + y * src_bilinear_samples, src_bilinear_samples,
611 max_sum_sq_error_fp16 = std::max(max_sum_sq_error_fp16, sum_sq_error_fp16);
612 if (max_sum_sq_error_fp16 > max_error) {
617 if (max_sum_sq_error_fp16 > max_error) {
618 fallback_to_fp32 = true;
619 src_bilinear_samples = combine_many_samples(weights, src_size, src_samples, dst_samples, &bilinear_weights_fp32);
622 // Encode as a two-component texture. Note the GL_REPEAT.
623 glActiveTexture(GL_TEXTURE0 + *sampler_num);
625 glBindTexture(GL_TEXTURE_2D, texnum);
627 if (last_texture_width == -1) {
628 // Need to set this state the first time.
629 glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
631 glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT);
633 glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT);
637 GLenum type, internal_format;
639 if (fallback_to_fp32) {
641 internal_format = GL_RG32F;
642 pixels = bilinear_weights_fp32;
644 type = GL_HALF_FLOAT;
645 internal_format = GL_RG16F;
646 pixels = bilinear_weights_fp16;
649 if (int(src_bilinear_samples) == last_texture_width &&
650 int(dst_samples) == last_texture_height &&
651 internal_format == last_texture_internal_format) {
652 // Texture dimensions and type are unchanged; it is more efficient
653 // to just update it rather than making an entirely new texture.
654 glTexSubImage2D(GL_TEXTURE_2D, 0, 0, 0, src_bilinear_samples, dst_samples, GL_RG, type, pixels);
656 glTexImage2D(GL_TEXTURE_2D, 0, internal_format, src_bilinear_samples, dst_samples, 0, GL_RG, type, pixels);
657 last_texture_width = src_bilinear_samples;
658 last_texture_height = dst_samples;
659 last_texture_internal_format = internal_format;
664 delete[] bilinear_weights_fp16;
665 delete[] bilinear_weights_fp32;
668 void SingleResamplePassEffect::set_gl_state(GLuint glsl_program_num, const string &prefix, unsigned *sampler_num)
670 Effect::set_gl_state(glsl_program_num, prefix, sampler_num);
672 assert(input_width > 0);
673 assert(input_height > 0);
674 assert(output_width > 0);
675 assert(output_height > 0);
677 if (input_width != last_input_width ||
678 input_height != last_input_height ||
679 output_width != last_output_width ||
680 output_height != last_output_height ||
681 offset != last_offset ||
683 update_texture(glsl_program_num, prefix, sampler_num);
684 last_input_width = input_width;
685 last_input_height = input_height;
686 last_output_width = output_width;
687 last_output_height = output_height;
688 last_offset = offset;
692 glActiveTexture(GL_TEXTURE0 + *sampler_num);
694 glBindTexture(GL_TEXTURE_2D, texnum);
697 uniform_sample_tex = *sampler_num;
699 uniform_num_samples = src_bilinear_samples;
700 uniform_num_loops = num_loops;
701 uniform_slice_height = slice_height;
703 // Instructions for how to convert integer sample numbers to positions in the weight texture.
704 uniform_sample_x_scale = 1.0f / src_bilinear_samples;
705 uniform_sample_x_offset = 0.5f / src_bilinear_samples;
707 if (direction == SingleResamplePassEffect::VERTICAL) {
708 uniform_whole_pixel_offset = lrintf(offset) / float(input_height);
710 uniform_whole_pixel_offset = lrintf(offset) / float(input_width);
713 // We specifically do not want mipmaps on the input texture;
714 // they break minification.
715 Node *self = chain->find_node_for_effect(this);
716 glActiveTexture(chain->get_input_sampler(self, 0));
718 glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);