From e0ea9226fa5ce390e7263f16c3e1812c8f768e1a Mon Sep 17 00:00:00 2001 From: shikhin Date: Tue, 5 Dec 2023 16:24:51 -0500 Subject: [PATCH] Switch to doubles. --- public/main.js | 4 +- src/main.cpp | 256 ++++++++++++++++++++++++------------------------- 2 files changed, 130 insertions(+), 130 deletions(-) diff --git a/public/main.js b/public/main.js index 3ccce37..261044e 100644 --- a/public/main.js +++ b/public/main.js @@ -163,7 +163,7 @@ function enhance() { } function to_float_arr(arr) { - const res = new Float32Array(arr.length) + const res = new Float64Array(arr.length) for (let i = 0; i < arr.length; i++) { res[i] = arr[i] } @@ -174,7 +174,7 @@ function transfer_matrix_to_heap() { const typed_array = to_float_arr(matrix_entries) const heap_pointer = Module._malloc(typed_array.length * typed_array.BYTES_PER_ELEMENT) - Module.HEAPF32.set(typed_array, heap_pointer >> 2) + Module.HEAPF64.set(typed_array, heap_pointer >> 3) return heap_pointer } diff --git a/src/main.cpp b/src/main.cpp index fe2378e..436c0ba 100644 --- a/src/main.cpp +++ b/src/main.cpp @@ -9,18 +9,18 @@ #include #include -const std::complex If(0.0f, 1.0f); +const std::complex If(0.0, 1.0); -const std::complex Omega(-1.0f/2.0f, std::sqrt(3.0f) / 2); -const std::complex Omega_sq(-1.0f/2.0f, -std::sqrt(3.0f) / 2); +const std::complex Omega(-1.0/2.0, std::sqrt(3.0) / 2); +const std::complex Omega_sq(-1.0/2.0, -std::sqrt(3.0) / 2); -const float eps = 1e-12; -const float PI = 3.141592653589793238463L; -const float M_2PI = 2*PI; +const double eps = 1e-12; +const double PI = 3.141592653589793238463L; +const double M_2PI = 2*PI; -float p_scale = 3; -float zoom_scale = 1; -float dr_scale; +double p_scale = 3; +double zoom_scale = 1; +double dr_scale; using emscripten::val; @@ -29,26 +29,26 @@ int d; size_t width, height; size_t num_threads; -float *output = nullptr; +double *output = nullptr; uint32_t *output_buffer = nullptr; thread_local const val document = val::global("document"); -std::array, 2> quadratic_solver(float a, float b, float c); +std::array, 2> quadratic_solver(double a, double b, double c); size_t EMSCRIPTEN_KEEPALIVE get_output_buffer() { return (size_t) output_buffer; } -float density_default(Eigen::MatrixXcf &A, Eigen::MatrixXcf &B, float a, float b) { - Eigen::MatrixXcf first = Eigen::MatrixXcf::Identity(A.rows(), A.cols()) - (((a / (a*a + b*b)) * A) + (b / (a*a + b*b) * B)); - Eigen::MatrixXcf second = (b * A - a * B).inverse(); +double density_default(Eigen::MatrixXcd &A, Eigen::MatrixXcd &B, double a, double b) { + Eigen::MatrixXcd first = Eigen::MatrixXcd::Identity(A.rows(), A.cols()) - (((a / (a*a + b*b)) * A) + (b / (a*a + b*b) * B)); + Eigen::MatrixXcd second = (b * A - a * B).inverse(); - Eigen::ComplexEigenSolver eigensolver(first * second, /* computeEigenvectors = */ false); + Eigen::ComplexEigenSolver eigensolver(first * second, /* computeEigenvectors = */ false); if (eigensolver.info() != Eigen::Success) { return 0; } auto eigenvalues = eigensolver.eigenvalues(); - float value = 0; + double value = 0; for(size_t i = 0; i < eigenvalues.rows(); i++) { if (std::abs(eigenvalues[i].imag()) > eps) { value += std::abs(eigenvalues[i].imag()); @@ -58,13 +58,13 @@ float density_default(Eigen::MatrixXcf &A, Eigen::MatrixXcf &B, float a, float b return value; } -float density_2(Eigen::MatrixXcf &A, Eigen::MatrixXcf &B, float a, float b, float precomp_coeffs[7]) { - //float tt0 = precomp_coeffs[0], tt1 = precomp_coeffs[1], tt00 = precomp_coeffs[2], tt01 = precomp_coeffs[3], +double density_2(Eigen::MatrixXcd &A, Eigen::MatrixXcd &B, double a, double b, double precomp_coeffs[7]) { + //double tt0 = precomp_coeffs[0], tt1 = precomp_coeffs[1], tt00 = precomp_coeffs[2], tt01 = precomp_coeffs[3], // tt11 = precomp_coeffs[4]; //auto roots = quadratic_solver(tt1*tt1 - tt11 - 2*tt1*b + 2*b*b, // -2*tt01 + 2*tt0*tt1 - 2*tt1*a - 2*tt0*b + 4*a*b, // tt0*tt0 - tt00 - 2*tt0*a + 2*a*a); - //float value = 0; + //double value = 0; //for (const auto &root : roots) { // if (root.imag() > eps) { // value += root.imag() / ((b * root + a) * std::conj(b * root + a)).real(); @@ -72,44 +72,44 @@ float density_2(Eigen::MatrixXcf &A, Eigen::MatrixXcf &B, float a, float b, floa //} //return value; - float value = precomp_coeffs[0] + precomp_coeffs[1]*b + precomp_coeffs[2]*b*b + precomp_coeffs[3]*a + double value = precomp_coeffs[0] + precomp_coeffs[1]*b + precomp_coeffs[2]*b*b + precomp_coeffs[3]*a + precomp_coeffs[4]*a*b + precomp_coeffs[5]*a*a; - if (value < eps) { return 0.0f; } + if (value < eps) { return 0.0; } - float x = (precomp_coeffs[6]*b*b + precomp_coeffs[7]*a*b + precomp_coeffs[8]*a*a); + double x = (precomp_coeffs[6]*b*b + precomp_coeffs[7]*a*b + precomp_coeffs[8]*a*a); value /= (x * x); return std::sqrt(value); } -float cubic_solver_cheat(float values[4]) { +double cubic_solver_cheat(double values[4]) { if (std::abs(values[3]) < eps) { if (std::abs(values[2]) < eps) { return 0; } - + auto D = values[1] * values[1] - 4 * values[0] * values[2]; if (D > eps) { return 0; } - return std::sqrt(-D) / (2.0f * values[2]); + return std::sqrt(-D) / (2.0 * values[2]); } - auto p = -values[2] / (3.0f * values[3]), - q = p*p*p + (values[1]*values[2] - 3.0f*values[0]*values[3]) / (6.0f*(values[3]*values[3])), - r = values[1] / (3.0f*values[3]); + auto p = -values[2] / (3.0 * values[3]), + q = p*p*p + (values[1]*values[2] - 3.0*values[0]*values[3]) / (6.0*(values[3]*values[3])), + r = values[1] / (3.0*values[3]); auto rp2 = (r - p*p), h = q*q + rp2*rp2*rp2; if (h < eps) { return 0; } h = std::sqrt(h); - return std::sqrt(3.0f) * std::abs(std::cbrt(q + h) - std::cbrt(q - h)) / (2.0f); + return std::sqrt(3.0) * std::abs(std::cbrt(q + h) - std::cbrt(q - h)) / (2.0); } -float density_3(Eigen::MatrixXcf &A, Eigen::MatrixXcf &B, float a, float b, float precomp_coeffs_1[7][7], - float precomp_coeffs_2[7][7], float precomp_coeffs_3[7][7], float precomp_coeffs_4[7][7]) { - float values[4] = { 0, 0, 0, 0 }; - float a_powers[7] = { 1, a, 0, 0, 0, 0, 0 }; - float b_powers[7] = { 1, b, 0, 0, 0, 0, 0 }; +double density_3(Eigen::MatrixXcd &A, Eigen::MatrixXcd &B, double a, double b, double precomp_coeffs_1[7][7], + double precomp_coeffs_2[7][7], double precomp_coeffs_3[7][7], double precomp_coeffs_4[7][7]) { + double values[4] = { 0, 0, 0, 0 }; + double a_powers[7] = { 1, a, 0, 0, 0, 0, 0 }; + double b_powers[7] = { 1, b, 0, 0, 0, 0, 0 }; for (size_t i = 2; i < 7; i += 1) { a_powers[i] = a_powers[i - 1] * a; @@ -118,7 +118,7 @@ float density_3(Eigen::MatrixXcf &A, Eigen::MatrixXcf &B, float a, float b, floa for (size_t i = 0; i < 7; i += 1) { for (size_t j = 0; j < 7; j += 1) { - float prod = a_powers[j] * b_powers[i]; + double prod = a_powers[j] * b_powers[i]; values[0] += precomp_coeffs_1[i][j] * prod; values[1] += precomp_coeffs_2[i][j] * prod; values[2] += precomp_coeffs_3[i][j] * prod; @@ -129,30 +129,30 @@ float density_3(Eigen::MatrixXcf &A, Eigen::MatrixXcf &B, float a, float b, floa return cubic_solver_cheat(values) / (a*a + b*b); } -std::array, 2> quadratic_solver(float a, float b, float c) { +std::array, 2> quadratic_solver(double a, double b, double c) { if (std::abs(a) < eps) { // todo - return std::array, 2> {0, 0}; + return std::array, 2> {0, 0}; } auto D = b*b - 4*a*c; if (D > eps) { - return std::array, 2> {(-b + std::sqrt(D)) / (2 * a), + return std::array, 2> {(-b + std::sqrt(D)) / (2 * a), (-b - std::sqrt(D)) / (2 * a)}; } else if (D < -eps) { - return std::array, 2> {(-b + If * std::sqrt(-D)) / (2 * a), + return std::array, 2> {(-b + If * std::sqrt(-D)) / (2 * a), (-b - If * std::sqrt(-D)) / (2 * a)}; } else { - return std::array, 2> {(-b) / (2 * a), (-b) / (2 * a)}; + return std::array, 2> {(-b) / (2 * a), (-b) / (2 * a)}; } } // first root returned is real -std::array, 3> cubic_solver(float d, float a, float b, float c, size_t &real_roots) { +std::array, 3> cubic_solver(double d, double a, double b, double c, size_t &real_roots) { // stolen from https://github.com/sasamil/Quartic/blob/master/quartic.cpp if (std::abs(d) < eps) { auto roots = quadratic_solver(a, b, c); - return std::array, 3> { roots[0], roots[1], 0 }; + return std::array, 3> { roots[0], roots[1], 0 }; } a /= d; b /= d; c /= d; @@ -168,59 +168,59 @@ std::array, 3> cubic_solver(float d, float a, float b, float t = std::acos(t); a /= 3; q = -2*std::sqrt(q); real_roots = 3; - return std::array, 3> { q*std::cos(t/3) - a, + return std::array, 3> { q*std::cos(t/3) - a, q*std::cos((t + M_2PI) / 3) - a, q*std::cos((t - M_2PI) / 3) - a }; } else { - float A = -std::pow(std::abs(r) + std::sqrt(r2 - q3), 1.0f/3); - float B; + double A = -std::pow(std::abs(r) + std::sqrt(r2 - q3), 1.0/3); + double B; if (r < 0) { A = -A; } if (std::abs(A) < eps) { B = 0; } else { B = q/A; } a /= 3; - float imaginary_part = 0.5 * std::sqrt(3.0) * (A - B); - float real_part = -0.5 * (A + B) - a; + double imaginary_part = 0.5 * std::sqrt(3.0) * (A - B); + double real_part = -0.5 * (A + B) - a; if (std::abs(imaginary_part) < eps) { real_roots = 3; - return std::array, 3> { (A + B) - a, + return std::array, 3> { (A + B) - a, real_part, real_part }; } else { real_roots = 1; - return std::array, 3> { (A + B) - a, + return std::array, 3> { (A + B) - a, real_part + If * imaginary_part, real_part - If * imaginary_part }; } } -/* auto p = -b / (3.0f * a), - q = p*p*p + (b*c - 3.0f*a*d) / (6.0f*(a*a)), - r = c / (3.0f*a); +/* auto p = -b / (3.0 * a), + q = p*p*p + (b*c - 3.0*a*d) / (6.0*(a*a)), + r = c / (3.0*a); auto rp2 = (r - p*p), h = q*q + rp2*rp2*rp2; - auto h_root = std::sqrt(h + If * 0.0f); - auto x = std::pow(q + h_root, 1.0f/3.0f); - return std::array, 3> {x - rp2 / x + p, Omega*x - rp2 / (Omega*x) + p, + auto h_root = std::sqrt(h + If * 0.0); + auto x = std::pow(q + h_root, 1.0/3.0); + return std::array, 3> {x - rp2 / x + p, Omega*x - rp2 / (Omega*x) + p, Omega_sq*x - rp2 / (Omega_sq*x) + p};*/ } -std::array, 4> quartic_solver(float e, float a, float b, float c, float d) { +std::array, 4> quartic_solver(double e, double a, double b, double c, double d) { // stolen from https://github.com/sasamil/Quartic/blob/master/quartic.cpp if (std::abs(e) < eps) { size_t trash; auto roots = cubic_solver(a, b, c, d, trash); - return std::array, 4> { roots[0], roots[1], roots[2], 0 }; + return std::array, 4> { roots[0], roots[1], roots[2], 0 }; } a /= e; b /= e; c /= e; d /= e; - float a3 = -b; - float b3 = a*c -4.*d; - float c3 = -a*a*d - c*c + 4.*b*d; + double a3 = -b; + double b3 = a*c -4.*d; + double c3 = -a*a*d - c*c + 4.*b*d; size_t iZeroes = 0; auto x3 = cubic_solver(1, a3, b3, c3, iZeroes); - float q1, q2, p1, p2, D, sqD, y = x3[0].real(); + double q1, q2, p1, p2, D, sqD, y = x3[0].real(); if (iZeroes > 1) { if (std::abs(x3[1].real()) > std::abs(y)) y = x3[1].real(); @@ -252,12 +252,12 @@ std::array, 4> quartic_solver(float e, float a, float b, flo return { first[0], first[1], second[0], second[1] }; } -float density_4(Eigen::MatrixXcf &A, Eigen::MatrixXcf &B, float a, float b, float precomp_coeffs_1[5][5], - float precomp_coeffs_2[5][5], float precomp_coeffs_3[5][5], float precomp_coeffs_4[5][5], - float precomp_coeffs_5[5][5]) { - float values[5] = { 0, 0, 0, 0, 0 }; - float a_powers[5] = { 1, a, a*a, 0, 0 }; - float b_powers[5] = { 1, b, b*b, 0, 0 }; +double density_4(Eigen::MatrixXcd &A, Eigen::MatrixXcd &B, double a, double b, double precomp_coeffs_1[5][5], + double precomp_coeffs_2[5][5], double precomp_coeffs_3[5][5], double precomp_coeffs_4[5][5], + double precomp_coeffs_5[5][5]) { + double values[5] = { 0, 0, 0, 0, 0 }; + double a_powers[5] = { 1, a, a*a, 0, 0 }; + double b_powers[5] = { 1, b, b*b, 0, 0 }; for (size_t i = 3; i < 5; i++) { a_powers[i] = a_powers[i - 1] * a; b_powers[i] = b_powers[i - 1] * b; @@ -265,7 +265,7 @@ float density_4(Eigen::MatrixXcf &A, Eigen::MatrixXcf &B, float a, float b, floa for (size_t i = 0; i < 5; i += 1) { for (size_t j = 0; j < 5; j += 1) { - float prod = a_powers[i] * b_powers[j]; + double prod = a_powers[i] * b_powers[j]; values[0] += precomp_coeffs_1[i][j] * prod; values[1] += precomp_coeffs_2[i][j] * prod; values[2] += precomp_coeffs_3[i][j] * prod; @@ -275,7 +275,7 @@ float density_4(Eigen::MatrixXcf &A, Eigen::MatrixXcf &B, float a, float b, floa } auto roots = quartic_solver(values[4], values[3], values[2], values[1], values[0]); - float value = 0; + double value = 0; for (const auto &root : roots) { if (root.imag() > eps) { value += root.imag() / ((a * root + b) * std::conj(a * root + b)).real(); @@ -284,62 +284,62 @@ float density_4(Eigen::MatrixXcf &A, Eigen::MatrixXcf &B, float a, float b, floa return value; } -void compute_output_thread(Eigen::MatrixXcf &A, Eigen::MatrixXcf &B, size_t idx) { +void compute_output_thread(Eigen::MatrixXcd &A, Eigen::MatrixXcd &B, size_t idx) { for (size_t i = (height / num_threads) * idx; i < (height / num_threads) * (idx + 1); i += 1) { for (size_t j = 0; j < width; j += 1) { - output[i * width + j] = density_default(A, B, dr_scale * ((j * 2.0f / width) - 1.0f), - -dr_scale * ((i * 2.0f / height) - 1.0f)); + output[i * width + j] = density_default(A, B, dr_scale * ((j * 2.0 / width) - 1.0), + -dr_scale * ((i * 2.0 / height) - 1.0)); } } } -void compute_output_thread_2(Eigen::MatrixXcf &A, Eigen::MatrixXcf &B, float precomp_coeffs[7], size_t idx) { +void compute_output_thread_2(Eigen::MatrixXcd &A, Eigen::MatrixXcd &B, double precomp_coeffs[7], size_t idx) { for (size_t i = (height / num_threads) * idx; i < (height / num_threads) * (idx + 1); i += 1) { for (size_t j = 0; j < width; j += 1) { - output[i * width + j] = density_2(A, B, dr_scale * ((j * 2.0f / width) - 1.0f), - -dr_scale * ((i * 2.0f / height) - 1.0f), precomp_coeffs); + output[i * width + j] = density_2(A, B, dr_scale * ((j * 2.0 / width) - 1.0), + -dr_scale * ((i * 2.0 / height) - 1.0), precomp_coeffs); } } } -void compute_output_thread_3(Eigen::MatrixXcf &A, Eigen::MatrixXcf &B, float precomp_coeffs_1[7][7], - float precomp_coeffs_2[7][7], float precomp_coeffs_3[7][7], float precomp_coeffs_4[7][7], +void compute_output_thread_3(Eigen::MatrixXcd &A, Eigen::MatrixXcd &B, double precomp_coeffs_1[7][7], + double precomp_coeffs_2[7][7], double precomp_coeffs_3[7][7], double precomp_coeffs_4[7][7], size_t idx) { for (size_t i = (height / num_threads) * idx; i < (height / num_threads) * (idx + 1); i += 1) { for (size_t j = 0; j < width; j += 1) { - output[i * width + j] = density_3(A, B, dr_scale * ((j * 2.0f / width) - 1.0f), - -dr_scale * ((i * 2.0f / height) - 1.0f), precomp_coeffs_1, + output[i * width + j] = density_3(A, B, dr_scale * ((j * 2.0 / width) - 1.0), + -dr_scale * ((i * 2.0 / height) - 1.0), precomp_coeffs_1, precomp_coeffs_2, precomp_coeffs_3, precomp_coeffs_4); } } } -void compute_output_thread_4(Eigen::MatrixXcf &A, Eigen::MatrixXcf &B, float precomp_coeffs_1[5][5], - float precomp_coeffs_2[5][5], float precomp_coeffs_3[5][5], float precomp_coeffs_4[5][5], - float precomp_coeffs_5[5][5], +void compute_output_thread_4(Eigen::MatrixXcd &A, Eigen::MatrixXcd &B, double precomp_coeffs_1[5][5], + double precomp_coeffs_2[5][5], double precomp_coeffs_3[5][5], double precomp_coeffs_4[5][5], + double precomp_coeffs_5[5][5], size_t idx) { for (size_t i = (height / num_threads) * idx; i < (height / num_threads) * (idx + 1); i += 1) { for (size_t j = 0; j < width; j += 1) { - output[i * width + j] = density_4(A, B, dr_scale * ((j * 2.0f / width) - 1.0f), - -dr_scale * ((i * 2.0f / height) - 1.0f), precomp_coeffs_1, + output[i * width + j] = density_4(A, B, dr_scale * ((j * 2.0 / width) - 1.0), + -dr_scale * ((i * 2.0 / height) - 1.0), precomp_coeffs_1, precomp_coeffs_2, precomp_coeffs_3, precomp_coeffs_4, precomp_coeffs_5); } } } -void compute_output(Eigen::MatrixXcf &C) { - Eigen::MatrixXcf A = (C + C.adjoint()) / 2.0f; - Eigen::MatrixXcf B = -If * (C - C.adjoint()) / 2.0f; +void compute_output(Eigen::MatrixXcd &C) { + Eigen::MatrixXcd A = (C + C.adjoint()) / 2.0; + Eigen::MatrixXcd B = -If * (C - C.adjoint()) / 2.0; std::thread *threads = new std::thread[num_threads]; if (d == 2) { - float A_tr = A.trace().real(); - float AA_tr = (A*A).trace().real(); - float B_tr = B.trace().real(); - float BB_tr = (B*B).trace().real(); - float AB_tr = (A*B).trace().real(); + double A_tr = A.trace().real(); + double AA_tr = (A*A).trace().real(); + double B_tr = B.trace().real(); + double BB_tr = (B*B).trace().real(); + double AB_tr = (A*B).trace().real(); - float precomp_coeffs[9] = { -AB_tr*AB_tr + 2*A_tr*B_tr*AB_tr - A_tr*A_tr*BB_tr - B_tr*B_tr*AA_tr + AA_tr*BB_tr, + double precomp_coeffs[9] = { -AB_tr*AB_tr + 2*A_tr*B_tr*AB_tr - A_tr*A_tr*BB_tr - B_tr*B_tr*AA_tr + AA_tr*BB_tr, 2*AA_tr*B_tr - 2*A_tr*AB_tr, A_tr*A_tr - 2*AA_tr, 2*BB_tr*A_tr - 2*B_tr*AB_tr, 4*AB_tr - 2*A_tr*B_tr, B_tr*B_tr - 2*BB_tr, @@ -349,9 +349,9 @@ void compute_output(Eigen::MatrixXcf &C) { threads[idx] = std::thread(compute_output_thread_2, std::ref(A), std::ref(B), precomp_coeffs, idx); } } else if (d == 3) { - float tr[4][4]; - Eigen::MatrixXcf A_powers[4] = { Eigen::MatrixXcf::Identity(A.rows(), A.cols()), A, A*A, Eigen::MatrixXcf::Identity(A.rows(), A.cols()) }; - Eigen::MatrixXcf B_powers[4] = { Eigen::MatrixXcf::Identity(B.rows(), B.cols()), B, B*B, Eigen::MatrixXcf::Identity(A.rows(), A.cols()) }; + double tr[4][4]; + Eigen::MatrixXcd A_powers[4] = { Eigen::MatrixXcd::Identity(A.rows(), A.cols()), A, A*A, Eigen::MatrixXcd::Identity(A.rows(), A.cols()) }; + Eigen::MatrixXcd B_powers[4] = { Eigen::MatrixXcd::Identity(B.rows(), B.cols()), B, B*B, Eigen::MatrixXcd::Identity(A.rows(), A.cols()) }; A_powers[3] = A_powers[2] * A; B_powers[3] = B_powers[2] * B; for (size_t i = 0; i < 4; i += 1) { @@ -360,7 +360,7 @@ void compute_output(Eigen::MatrixXcf &C) { } } - float precomp_coeffs_1[7][7] = {{0, 0, 0, -(tr[1][0]*tr[1][0]*tr[1][0]) + 3*tr[1][0]*tr[2][0] - + double precomp_coeffs_1[7][7] = {{0, 0, 0, -(tr[1][0]*tr[1][0]*tr[1][0]) + 3*tr[1][0]*tr[2][0] - 2*tr[3][0], 3*(tr[1][0]*tr[1][0]) - 3*tr[2][0], -6*tr[1][0], 6}, {0, 0, -3*tr[0][1]*(tr[1][0]*tr[1][0]) + 6*tr[1][0]*tr[1][1] + 3*tr[0][1]*tr[2][0] - 6*tr[2][1], 6*tr[0][1]*tr[1][0] - 6*tr[1][1], @@ -374,7 +374,7 @@ void compute_output(Eigen::MatrixXcf &C) { {-6*tr[0][1], 0, 0, 0, 0, 0, 0}, {6, 0, 0, 0, 0, 0, 0}}; - float precomp_coeffs_2[7][7] = {{0, 0, 0, -3*tr[0][1]*tr[1][0]*tr[1][0] + + double precomp_coeffs_2[7][7] = {{0, 0, 0, -3*tr[0][1]*tr[1][0]*tr[1][0] + 6*tr[1][0]*tr[1][1] + 3*tr[0][1]*tr[2][0] - 6*tr[2][1], 6*tr[0][1]*tr[1][0] - 6*tr[1][1], -6*tr[0][1], 0}, {0, 0, -6*tr[0][1]*tr[0][1]*tr[1][0] + 6*tr[0][2]*tr[1][0] + 3*tr[1][0]*tr[1][0]*tr[1][0] + @@ -391,7 +391,7 @@ void compute_output(Eigen::MatrixXcf &C) { {6*tr[1][0], 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0}}; - float precomp_coeffs_3[7][7] = {{0, 0, 0, -3*tr[0][1]*tr[0][1]*tr[1][0] + + double precomp_coeffs_3[7][7] = {{0, 0, 0, -3*tr[0][1]*tr[0][1]*tr[1][0] + 3*tr[0][2]*tr[1][0] + 6*tr[0][1]*tr[1][1] - 6*tr[1][2], 3*tr[0][1]*tr[0][1] - 3*tr[0][2], 0, 0}, {0, 0, -3*tr[0][1]*tr[0][1]*tr[0][1] + 9*tr[0][1]*tr[0][2] - 6*tr[0][3] + @@ -406,7 +406,7 @@ void compute_output(Eigen::MatrixXcf &C) { {0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0}}; - float precomp_coeffs_4[7][7] = {{0, 0, 0, -(tr[0][1]*tr[0][1]*tr[0][1]) + 3*tr[0][1]*tr[0][2] - + double precomp_coeffs_4[7][7] = {{0, 0, 0, -(tr[0][1]*tr[0][1]*tr[0][1]) + 3*tr[0][1]*tr[0][2] - 2*tr[0][3], 0, 0, 0}, {0, 0, 3*tr[0][1]*tr[0][1]*tr[1][0] - 3*tr[0][2]*tr[1][0] - 6*tr[0][1]*tr[1][1] + 6*tr[1][2], 0, 0, 0, 0}, @@ -422,45 +422,45 @@ void compute_output(Eigen::MatrixXcf &C) { precomp_coeffs_2, precomp_coeffs_3, precomp_coeffs_4, idx); } } else if (d == 4) { - float tt0 = A.trace().real(); - float tt1 = B.trace().real(); - float tt00 = (A*A).trace().real(); - float tt01 = (A*B).trace().real(); - float tt11 = (B*B).trace().real(); - float tt000 = (A*A*A).trace().real(); - float tt001 = (A*A*B).trace().real(); - float tt011 = (A*B*B).trace().real(); - float tt111 = (B*B*B).trace().real(); - float tt0000 = (A*A*A*A).trace().real(); - float tt0001 = (A*A*A*B).trace().real(); - float tt0011 = (A*A*B*B).trace().real(); - float tt0101 = (A*B*A*B).trace().real(); - float tt0111 = (A*B*B*B).trace().real(); - float tt1111 = (B*B*B*B).trace().real(); + double tt0 = A.trace().real(); + double tt1 = B.trace().real(); + double tt00 = (A*A).trace().real(); + double tt01 = (A*B).trace().real(); + double tt11 = (B*B).trace().real(); + double tt000 = (A*A*A).trace().real(); + double tt001 = (A*A*B).trace().real(); + double tt011 = (A*B*B).trace().real(); + double tt111 = (B*B*B).trace().real(); + double tt0000 = (A*A*A*A).trace().real(); + double tt0001 = (A*A*A*B).trace().real(); + double tt0011 = (A*A*B*B).trace().real(); + double tt0101 = (A*B*A*B).trace().real(); + double tt0111 = (A*B*B*B).trace().real(); + double tt1111 = (B*B*B*B).trace().real(); - float precomp0[5][5] = {{tt1*tt1*tt1*tt1 - 6*tt1*tt1*tt11 + 3*tt11*tt11 + 8*tt1*tt111 - 6*tt1111,-4*tt1*tt1*tt1 + 12*tt1*tt11 - 8*tt111,12*tt1*tt1 - 12*tt11,-24*tt1,24}, + double precomp0[5][5] = {{tt1*tt1*tt1*tt1 - 6*tt1*tt1*tt11 + 3*tt11*tt11 + 8*tt1*tt111 - 6*tt1111,-4*tt1*tt1*tt1 + 12*tt1*tt11 - 8*tt111,12*tt1*tt1 - 12*tt11,-24*tt1,24}, {0,0,0,0,0}, {0,0,0,0,0}, {0,0,0,0,0}, {0,0,0,0,0}}; - float precomp1[5][5] = {{-24*tt0111 + 24*tt011*tt1 - 12*tt01*tt1*tt1 + 4*tt0*tt1*tt1*tt1 + 12*tt01*tt11 - 12*tt0*tt1*tt11 + 8*tt0*tt111,- 24*tt011 + 24*tt01*tt1 - 12*tt0*tt1*tt1 + 12*tt0*tt11,-24*tt01 + 24*tt0*tt1,-24*tt0,0},{-4*tt1*tt1*tt1 + 12*tt1*tt11 - 8*tt111,24*tt1*tt1 - 24*tt11,-72*tt1,96,0}, + double precomp1[5][5] = {{-24*tt0111 + 24*tt011*tt1 - 12*tt01*tt1*tt1 + 4*tt0*tt1*tt1*tt1 + 12*tt01*tt11 - 12*tt0*tt1*tt11 + 8*tt0*tt111,- 24*tt011 + 24*tt01*tt1 - 12*tt0*tt1*tt1 + 12*tt0*tt11,-24*tt01 + 24*tt0*tt1,-24*tt0,0},{-4*tt1*tt1*tt1 + 12*tt1*tt11 - 8*tt111,24*tt1*tt1 - 24*tt11,-72*tt1,96,0}, {0,0,0,0,0}, {0,0,0,0,0}, {0,0,0,0,0}}; - float precomp2[5][5] = {{-24*tt0011 + 12*tt01*tt01 - 12*tt0101 + 24*tt0*tt011 + 24*tt001*tt1 - 24*tt0*tt01*tt1 + 6*tt0*tt0*tt1*tt1 - 6*tt00*tt1*tt1 - 6*tt0*tt0*tt11 + 6*tt00*tt11,-24*tt001 + 24*tt0*tt01 - 12*tt0*tt0*tt1 + 12*tt00*tt1,12*tt0*tt0 - 12*tt00,0,0}, + double precomp2[5][5] = {{-24*tt0011 + 12*tt01*tt01 - 12*tt0101 + 24*tt0*tt011 + 24*tt001*tt1 - 24*tt0*tt01*tt1 + 6*tt0*tt0*tt1*tt1 - 6*tt00*tt1*tt1 - 6*tt0*tt0*tt11 + 6*tt00*tt11,-24*tt001 + 24*tt0*tt01 - 12*tt0*tt0*tt1 + 12*tt00*tt1,12*tt0*tt0 - 12*tt00,0,0}, {- 24*tt011 + 24*tt01*tt1 - 12*tt0*tt1*tt1 + 12*tt0*tt11,-48*tt01 + 48*tt0*tt1,-72*tt0,0,0}, {12*tt1*tt1 - 12*tt11,-72*tt1,144,0,0}, {0,0,0,0,0}, {0,0,0,0,0}}; - float precomp3[5][5] = {{-24*tt0001 + 24*tt0*tt001 - 12*tt0*tt0*tt01 + 12*tt00*tt01 + 4*tt0*tt0*tt0*tt1 - 12*tt0*tt00*tt1 + 8*tt000*tt1,-4*tt0*tt0*tt0 + 12*tt0*tt00 - 8*tt000,0,0,0}, + double precomp3[5][5] = {{-24*tt0001 + 24*tt0*tt001 - 12*tt0*tt0*tt01 + 12*tt00*tt01 + 4*tt0*tt0*tt0*tt1 - 12*tt0*tt00*tt1 + 8*tt000*tt1,-4*tt0*tt0*tt0 + 12*tt0*tt00 - 8*tt000,0,0,0}, {-24*tt001 + 24*tt0*tt01 - 12*tt0*tt0*tt1 + 12*tt00*tt1,24*tt0*tt0 - 24*tt00,0,0,0},{-24*tt01 + 24*tt0*tt1,-72*tt0,0,0,0}, {-24*tt1,96,0,0,0}, {0,0,0,0,0}}; - float precomp4[5][5] = {{tt0*tt0*tt0*tt0 - 6*tt0*tt0*tt00 + 3*tt00*tt00 + 8*tt0*tt000 - 6*tt0000,0,0,0,0}, + double precomp4[5][5] = {{tt0*tt0*tt0*tt0 - 6*tt0*tt0*tt00 + 3*tt00*tt00 + 8*tt0*tt000 - 6*tt0000,0,0,0,0}, {-4*tt0*tt0*tt0 + 12*tt0*tt00 - 8*tt000,0,0,0,0},{12*tt0*tt0 - 12*tt00,0,0,0,0}, {-24*tt0,0,0,0,0}, {24,0,0,0,0}}; @@ -481,14 +481,14 @@ void compute_output(Eigen::MatrixXcf &C) { for (size_t i = 0; i < height; i += 1) { for (size_t j = 0; j < width; j += 1) { - float comp = 40.0f * output[i * width + j] / (1 + 40.0f * output[i * width + j]); - uint32_t comp_255 = (uint32_t)((uint8_t)(comp * 255.0f)); + double comp = 40.0 * output[i * width + j] / (1 + 40.0 * output[i * width + j]); + uint32_t comp_255 = (uint32_t)((uint8_t)(comp * 255.0)); output_buffer[i * width + j] = (0x000000FF | ((255 - comp_255) << 8) | ((255 - comp_255) << 16) | (comp_255 << 24)) ^ (comp_255 >> 1); } } - Eigen::ComplexEigenSolver eigensolver(A.inverse() * B); + Eigen::ComplexEigenSolver eigensolver(A.inverse() * B); if (eigensolver.info() != Eigen::Success) { return; } auto eigenvectors = eigensolver.eigenvectors(); @@ -501,7 +501,7 @@ void compute_output(Eigen::MatrixXcf &C) { } } -void EMSCRIPTEN_KEEPALIVE set_zoom(float zoom) { +void EMSCRIPTEN_KEEPALIVE set_zoom(double zoom) { zoom_scale = zoom; } @@ -509,8 +509,8 @@ void EMSCRIPTEN_KEEPALIVE set_matrix(size_t dim, size_t pointer) { d = dim; dr_scale = zoom_scale * dim * p_scale; - float *entries = (float*)pointer; - Eigen::MatrixXcf C = Eigen::MatrixXcf::Zero(d, d); + double *entries = (double*)pointer; + Eigen::MatrixXcd C = Eigen::MatrixXcd::Zero(d, d); for (size_t i = 0; i < d; i++) { for (size_t j = 0; j < d; j++) { C(i, j) = entries[2 * (i * d + j)] + entries[2 * (i * d + j) + 1] * If; @@ -525,9 +525,9 @@ void set_resolution(size_t resolution) { delete output_buffer; width = height = resolution; - output = new float[width * height]; + output = new double[width * height]; output_buffer = new uint32_t[width * height]; - std::memset(output, 0, width * height * sizeof(float)); + std::memset(output, 0, width * height * sizeof(double)); } int main() {