--- /dev/null
+// Unit tests for FFTPassEffect.
+
+#include <math.h>
+
+#include "effect_chain.h"
+#include "gtest/gtest.h"
+#include "image_format.h"
+#include "fft_pass_effect.h"
+#include "multiply_effect.h"
+#include "test_util.h"
+
+namespace {
+
+// Generate a random number uniformly distributed between [-1.0, 1.0].
+float uniform_random()
+{
+ return 2.0 * ((float)rand() / RAND_MAX - 0.5);
+}
+
+void setup_fft(EffectChain *chain, int fft_size, bool inverse,
+ bool add_normalizer = false,
+ FFTPassEffect::Direction direction = FFTPassEffect::HORIZONTAL)
+{
+ assert((fft_size & (fft_size - 1)) == 0); // Must be power of two.
+ for (int i = 1, subsize = 2; subsize <= fft_size; ++i, subsize *= 2) {
+ Effect *fft_effect = chain->add_effect(new FFTPassEffect());
+ bool ok = fft_effect->set_int("fft_size", fft_size);
+ ok |= fft_effect->set_int("pass_number", i);
+ ok |= fft_effect->set_int("inverse", inverse);
+ ok |= fft_effect->set_int("direction", direction);
+ assert(ok);
+ }
+
+ if (add_normalizer) {
+ float factor[4] = { 1.0f / fft_size, 1.0f / fft_size, 1.0f / fft_size, 1.0f / fft_size };
+ Effect *multiply_effect = chain->add_effect(new MultiplyEffect());
+ bool ok = multiply_effect->set_vec4("factor", factor);
+ assert(ok);
+ }
+}
+
+void run_fft(const float *in, float *out, int fft_size, bool inverse,
+ bool add_normalizer = false,
+ FFTPassEffect::Direction direction = FFTPassEffect::HORIZONTAL)
+{
+ int width, height;
+ if (direction == FFTPassEffect::HORIZONTAL) {
+ width = fft_size;
+ height = 1;
+ } else {
+ width = 1;
+ height = fft_size;
+ }
+ EffectChainTester tester(in, width, height, FORMAT_RGBA_PREMULTIPLIED_ALPHA, COLORSPACE_sRGB, GAMMA_LINEAR);
+ setup_fft(tester.get_chain(), fft_size, inverse, add_normalizer, direction);
+ tester.run(out, GL_RGBA, COLORSPACE_sRGB, GAMMA_LINEAR, OUTPUT_ALPHA_FORMAT_PREMULTIPLIED);
+}
+
+} // namespace
+
+TEST(FFTPassEffectTest, ZeroStaysZero) {
+ const int fft_size = 64;
+ float data[fft_size * 4] = { 0 };
+ float out_data[fft_size * 4];
+
+ run_fft(data, out_data, fft_size, false);
+ expect_equal(data, out_data, 4, fft_size);
+
+ run_fft(data, out_data, fft_size, true);
+ expect_equal(data, out_data, 4, fft_size);
+}
+
+TEST(FFTPassEffectTest, Impulse) {
+ const int fft_size = 64;
+ float data[fft_size * 4] = { 0 };
+ float expected_data[fft_size * 4], out_data[fft_size * 4];
+ data[0] = 1.0;
+ data[1] = 1.2;
+ data[2] = 1.4;
+ data[3] = 3.0;
+
+ for (int i = 0; i < fft_size; ++i) {
+ expected_data[i * 4 + 0] = data[0];
+ expected_data[i * 4 + 1] = data[1];
+ expected_data[i * 4 + 2] = data[2];
+ expected_data[i * 4 + 3] = data[3];
+ }
+
+ run_fft(data, out_data, fft_size, false);
+ expect_equal(expected_data, out_data, 4, fft_size);
+
+ run_fft(data, out_data, fft_size, true);
+ expect_equal(expected_data, out_data, 4, fft_size);
+}
+
+TEST(FFTPassEffectTest, SingleFrequency) {
+ const int fft_size = 16;
+ float data[fft_size * 4] = { 0 };
+ float expected_data[fft_size * 4], out_data[fft_size * 4];
+ for (int i = 0; i < fft_size; ++i) {
+ data[i * 4 + 0] = sin(2.0 * M_PI * (4.0 * i) / fft_size);
+ data[i * 4 + 1] = 0.0;
+ data[i * 4 + 2] = 0.0;
+ data[i * 4 + 3] = 0.0;
+ }
+ for (int i = 0; i < fft_size; ++i) {
+ expected_data[i * 4 + 0] = 0.0;
+ expected_data[i * 4 + 1] = 0.0;
+ expected_data[i * 4 + 2] = 0.0;
+ expected_data[i * 4 + 3] = 0.0;
+ }
+ expected_data[4 * 4 + 1] = -8.0;
+ expected_data[12 * 4 + 1] = 8.0;
+
+ run_fft(data, out_data, fft_size, false, false, FFTPassEffect::HORIZONTAL);
+ expect_equal(expected_data, out_data, 4, fft_size);
+
+ run_fft(data, out_data, fft_size, false, false, FFTPassEffect::VERTICAL);
+ expect_equal(expected_data, out_data, 4, fft_size);
+}
+
+TEST(FFTPassEffectTest, Repeat) {
+ const int fft_size = 64;
+ const int num_repeats = 31; // Prime, to make things more challenging.
+ float data[num_repeats * fft_size * 4] = { 0 };
+ float expected_data[num_repeats * fft_size * 4], out_data[num_repeats * fft_size * 4];
+
+ srand(12345);
+ for (int i = 0; i < num_repeats * fft_size * 4; ++i) {
+ data[i] = uniform_random();
+ }
+
+ for (int i = 0; i < num_repeats; ++i) {
+ run_fft(data + i * fft_size * 4, expected_data + i * fft_size * 4, fft_size, false);
+ }
+
+ {
+ // Horizontal.
+ EffectChainTester tester(data, num_repeats * fft_size, 1, FORMAT_RGBA_PREMULTIPLIED_ALPHA, COLORSPACE_sRGB, GAMMA_LINEAR);
+ setup_fft(tester.get_chain(), fft_size, false);
+ tester.run(out_data, GL_RGBA, COLORSPACE_sRGB, GAMMA_LINEAR, OUTPUT_ALPHA_FORMAT_PREMULTIPLIED);
+
+ expect_equal(expected_data, out_data, 4, num_repeats * fft_size);
+ }
+ {
+ // Vertical.
+ EffectChainTester tester(data, 1, num_repeats * fft_size, FORMAT_RGBA_PREMULTIPLIED_ALPHA, COLORSPACE_sRGB, GAMMA_LINEAR);
+ setup_fft(tester.get_chain(), fft_size, false, false, FFTPassEffect::VERTICAL);
+ tester.run(out_data, GL_RGBA, COLORSPACE_sRGB, GAMMA_LINEAR, OUTPUT_ALPHA_FORMAT_PREMULTIPLIED);
+
+ expect_equal(expected_data, out_data, 4, num_repeats * fft_size);
+ }
+}
+
+TEST(FFTPassEffectTest, TwoDimensional) { // Implicitly tests vertical.
+ srand(1234);
+ const int fft_size = 16;
+ float in[fft_size * fft_size * 4], out[fft_size * fft_size * 4], expected_out[fft_size * fft_size * 4];
+ for (int y = 0; y < fft_size; ++y) {
+ for (int x = 0; x < fft_size; ++x) {
+ in[(y * fft_size + x) * 4 + 0] =
+ sin(2.0 * M_PI * (2 * x + 3 * y) / fft_size);
+ in[(y * fft_size + x) * 4 + 1] = 0.0;
+ in[(y * fft_size + x) * 4 + 2] = 0.0;
+ in[(y * fft_size + x) * 4 + 3] = 0.0;
+ }
+ }
+ memset(expected_out, 0, sizeof(expected_out));
+
+ // This result has been verified using the fft2() function in Octave,
+ // which uses FFTW.
+ expected_out[(3 * fft_size + 2) * 4 + 1] = -128.0;
+ expected_out[(13 * fft_size + 14) * 4 + 1] = 128.0;
+
+ EffectChainTester tester(in, fft_size, fft_size, FORMAT_RGBA_PREMULTIPLIED_ALPHA, COLORSPACE_sRGB, GAMMA_LINEAR);
+ setup_fft(tester.get_chain(), fft_size, false, false, FFTPassEffect::HORIZONTAL);
+ setup_fft(tester.get_chain(), fft_size, false, false, FFTPassEffect::VERTICAL);
+ tester.run(out, GL_RGBA, COLORSPACE_sRGB, GAMMA_LINEAR, OUTPUT_ALPHA_FORMAT_PREMULTIPLIED);
+
+ expect_equal(expected_out, out, 4 * fft_size, fft_size, 0.25, 0.0005);
+}
+
+// The classic paper for FFT correctness testing is Funda Ergün:
+// “Testing Multivariate Linear Functions: Overcoming the Generator Bottleneck”
+// (http://www.cs.sfu.ca/~funda/PUBLICATIONS/stoc95.ps), which proves that
+// testing three basic properties of FFTs guarantees that the function is
+// correct (at least under the assumption that errors are random).
+//
+// We don't follow the paper directly, though, for a few reasons: First,
+// Ergün's paper really considers _self-correcting_ systems, which may
+// be stochastically faulty, and thus uses various relatively complicated
+// bounds and tests we don't really need. Second, the FFTs it considers
+// are all about polynomials over finite fields, which means that results
+// are exact and thus easy to test; we work with floats (half-floats!),
+// and thus need some error tolerance.
+//
+// So instead, we follow the implementation of FFTW, which is really the
+// gold standard when it comes to FFTs these days. They hard-code 20
+// testing rounds as opposed to the more complicated bounds in the paper,
+// and have a simpler version of the third test.
+//
+// The error bounds are set somewhat empirically, but remember that these
+// inputs will give frequency values as large as ~16, where 0.025 is
+// within the 9th bit (of 11 total mantissa bits in fp16).
+const int ergun_rounds = 20;
+
+// Test 1: Test that FFT(a + b) = FFT(a) + FFT(b).
+TEST(FFTPassEffectTest, ErgunLinearityTest) {
+ srand(1234);
+ const int max_fft_size = 64;
+ float a[max_fft_size * 4], b[max_fft_size * 4], sum[max_fft_size * 4];
+ float a_out[max_fft_size * 4], b_out[max_fft_size * 4], sum_out[max_fft_size * 4], expected_sum_out[max_fft_size * 4];
+ for (int fft_size = 2; fft_size <= max_fft_size; fft_size *= 2) {
+ for (int inverse = 0; inverse <= 1; ++inverse) {
+ for (int i = 0; i < ergun_rounds; ++i) {
+ for (int j = 0; j < fft_size * 4; ++j) {
+ a[j] = uniform_random();
+ b[j] = uniform_random();
+ }
+ run_fft(a, a_out, fft_size, inverse);
+ run_fft(b, b_out, fft_size, inverse);
+
+ for (int j = 0; j < fft_size * 4; ++j) {
+ sum[j] = a[j] + b[j];
+ expected_sum_out[j] = a_out[j] + b_out[j];
+ }
+
+ run_fft(sum, sum_out, fft_size, inverse);
+ expect_equal(expected_sum_out, sum_out, 4, fft_size, 0.03, 0.0005);
+ }
+ }
+ }
+}
+
+// Test 2: Test that FFT(delta(i)) = 1 (where delta(i) = [1 0 0 0 ...]),
+// or more specifically, test that FFT(a + delta(i)) - FFT(a) = 1.
+TEST(FFTPassEffectTest, ErgunImpulseTransform) {
+ srand(1235);
+ const int max_fft_size = 64;
+ float a[max_fft_size * 4], b[max_fft_size * 4];
+ float a_out[max_fft_size * 4], b_out[max_fft_size * 4], sum_out[max_fft_size * 4], expected_sum_out[max_fft_size * 4];
+ for (int fft_size = 2; fft_size <= max_fft_size; fft_size *= 2) {
+ for (int inverse = 0; inverse <= 1; ++inverse) {
+ for (int i = 0; i < ergun_rounds; ++i) {
+ for (int j = 0; j < fft_size * 4; ++j) {
+ a[j] = uniform_random();
+
+ // Compute delta(j) - a.
+ if (j < 4) {
+ b[j] = 1.0 - a[j];
+ } else {
+ b[j] = -a[j];
+ }
+ }
+ run_fft(a, a_out, fft_size, inverse);
+ run_fft(b, b_out, fft_size, inverse);
+
+ for (int j = 0; j < fft_size * 4; ++j) {
+ sum_out[j] = a_out[j] + b_out[j];
+ expected_sum_out[j] = 1.0;
+ }
+ expect_equal(expected_sum_out, sum_out, 4, fft_size, 0.025, 0.0005);
+ }
+ }
+ }
+}
+
+// Test 3: Test the time-shift property of the FFT, in that a circular left-shift
+// multiplies the result by e^(j 2pi k/N) (linear phase adjustment).
+// As fftw_test.c says, “The paper performs more tests, but this code should be
+// fine too”.
+TEST(FFTPassEffectTest, ErgunShiftProperty) {
+ srand(1236);
+ const int max_fft_size = 64;
+ float a[max_fft_size * 4], b[max_fft_size * 4];
+ float a_out[max_fft_size * 4], b_out[max_fft_size * 4], expected_a_out[max_fft_size * 4];
+ for (int fft_size = 2; fft_size <= max_fft_size; fft_size *= 2) {
+ for (int inverse = 0; inverse <= 1; ++inverse) {
+ for (int direction = 0; direction <= 1; ++direction) {
+ for (int i = 0; i < ergun_rounds; ++i) {
+ for (int j = 0; j < fft_size * 4; ++j) {
+ a[j] = uniform_random();
+ }
+
+ // Circular shift left by one step.
+ for (int j = 0; j < fft_size * 4; ++j) {
+ b[j] = a[(j + 4) % (fft_size * 4)];
+ }
+ run_fft(a, a_out, fft_size, inverse, false, FFTPassEffect::Direction(direction));
+ run_fft(b, b_out, fft_size, inverse, false, FFTPassEffect::Direction(direction));
+
+ for (int j = 0; j < fft_size; ++j) {
+ double s = -sin(j * 2.0 * M_PI / fft_size);
+ double c = cos(j * 2.0 * M_PI / fft_size);
+ if (inverse) {
+ s = -s;
+ }
+
+ expected_a_out[j * 4 + 0] = b_out[j * 4 + 0] * c - b_out[j * 4 + 1] * s;
+ expected_a_out[j * 4 + 1] = b_out[j * 4 + 0] * s + b_out[j * 4 + 1] * c;
+
+ expected_a_out[j * 4 + 2] = b_out[j * 4 + 2] * c - b_out[j * 4 + 3] * s;
+ expected_a_out[j * 4 + 3] = b_out[j * 4 + 2] * s + b_out[j * 4 + 3] * c;
+ }
+ expect_equal(expected_a_out, a_out, 4, fft_size, 0.025, 0.0005);
+ }
+ }
+ }
+ }
+}
+
+TEST(FFTPassEffectTest, BigFFTAccuracy) {
+ srand(1234);
+ const int max_fft_size = 2048;
+ float in[max_fft_size * 4], out[max_fft_size * 4], out2[max_fft_size * 4];
+ for (int fft_size = 2; fft_size <= max_fft_size; fft_size *= 2) {
+ for (int j = 0; j < fft_size * 4; ++j) {
+ in[j] = uniform_random();
+ }
+ run_fft(in, out, fft_size, false, true); // Forward, with normalization.
+ run_fft(out, out2, fft_size, true); // Reverse.
+
+ // These error bounds come from
+ // http://en.wikipedia.org/wiki/Fast_Fourier_transform#Accuracy_and_approximations,
+ // with empirically estimated epsilons. Note that the calculated
+ // rms in expect_equal() is divided by sqrt(N), so we compensate
+ // similarly here.
+ double max_error = 0.0009 * log2(fft_size);
+ double rms_limit = 0.0007 * sqrt(log2(fft_size)) / sqrt(fft_size);
+ expect_equal(in, out2, 4, fft_size, max_error, rms_limit);
+ }
+}
projects / movit / blobdiff