| /* |
| * Copyright 2020 Google Inc. |
| * |
| * Use of this source code is governed by a BSD-style license that can be |
| * found in the LICENSE file. |
| */ |
| |
| #include "include/utils/SkRandom.h" |
| #include "src/core/SkGeometry.h" |
| #include "src/gpu/GrVx.h" |
| #include "tests/Test.h" |
| #include <limits> |
| #include <numeric> |
| |
| using namespace grvx; |
| using skvx::bit_pun; |
| |
| DEF_TEST(grvx_cross_dot, r) { |
| REPORTER_ASSERT(r, grvx::cross({0,1}, {0,1}) == 0); |
| REPORTER_ASSERT(r, grvx::cross({1,0}, {1,0}) == 0); |
| REPORTER_ASSERT(r, grvx::cross({1,1}, {1,1}) == 0); |
| REPORTER_ASSERT(r, grvx::cross({1,1}, {1,-1}) == -2); |
| REPORTER_ASSERT(r, grvx::cross({1,1}, {-1,1}) == 2); |
| |
| REPORTER_ASSERT(r, grvx::dot({0,1}, {1,0}) == 0); |
| REPORTER_ASSERT(r, grvx::dot({1,0}, {0,1}) == 0); |
| REPORTER_ASSERT(r, grvx::dot({1,1}, {1,-1}) == 0); |
| REPORTER_ASSERT(r, grvx::dot({1,1}, {1,1}) == 2); |
| REPORTER_ASSERT(r, grvx::dot({1,1}, {-1,-1}) == -2); |
| |
| SkRandom rand; |
| for (int i = 0; i < 100; ++i) { |
| float a=rand.nextRangeF(-1,1), b=rand.nextRangeF(-1,1), c=rand.nextRangeF(-1,1), |
| d=rand.nextRangeF(-1,1); |
| constexpr static float kTolerance = 1.f / (1 << 20); |
| REPORTER_ASSERT(r, SkScalarNearlyEqual( |
| grvx::cross({a,b}, {c,d}), SkPoint::CrossProduct({a,b}, {c,d}), kTolerance)); |
| REPORTER_ASSERT(r, SkScalarNearlyEqual( |
| grvx::dot({a,b}, {c,d}), SkPoint::DotProduct({a,b}, {c,d}), kTolerance)); |
| } |
| } |
| |
| static bool check_approx_acos(skiatest::Reporter* r, float x, float approx_acos_x) { |
| float acosf_x = acosf(x); |
| float error = acosf_x - approx_acos_x; |
| if (!(fabsf(error) <= GRVX_FAST_ACOS_MAX_ERROR)) { |
| ERRORF(r, "Larger-than-expected error from grvx::approx_acos\n" |
| " x= %f\n" |
| " approx_acos_x= %f (%f degrees\n" |
| " acosf_x= %f (%f degrees\n" |
| " error= %f (%f degrees)\n" |
| " tolerance= %f (%f degrees)\n\n", |
| x, approx_acos_x, SkRadiansToDegrees(approx_acos_x), acosf_x, |
| SkRadiansToDegrees(acosf_x), error, SkRadiansToDegrees(error), |
| GRVX_FAST_ACOS_MAX_ERROR, SkRadiansToDegrees(GRVX_FAST_ACOS_MAX_ERROR)); |
| return false; |
| } |
| return true; |
| } |
| |
| DEF_TEST(grvx_approx_acos, r) { |
| float4 boundaries = approx_acos(float4{-1, 0, 1, 0}); |
| check_approx_acos(r, -1, boundaries[0]); |
| check_approx_acos(r, 0, boundaries[1]); |
| check_approx_acos(r, +1, boundaries[2]); |
| |
| // Select a distribution of starting points around which to begin testing approx_acos. These |
| // fall roughly around the known minimum and maximum errors. No need to include -1, 0, or 1 |
| // since those were just tested above. (Those are tricky because 0 is an inflection and the |
| // derivative is infinite at 1 and -1.) |
| constexpr static int N = 8; |
| vec<8> x = {-.99f, -.8f, -.4f, -.2f, .2f, .4f, .8f, .99f}; |
| |
| // Converge at the various local minima and maxima of "approx_acos(x) - cosf(x)" and verify that |
| // approx_acos is always within "kTolerance" degrees of the expected answer. |
| vec<N> err_; |
| for (int iter = 0; iter < 10; ++iter) { |
| // Run our approximate inverse cosine approximation. |
| vec<N> approx_acos_x = approx_acos(x); |
| |
| // Find d/dx(error) |
| // = d/dx(approx_acos(x) - acos(x)) |
| // = (f'g - fg')/gg + 1/sqrt(1 - x^2), [where f = bx^3 + ax, g = dx^4 + cx^2 + 1] |
| vec<N> xx = x*x; |
| vec<N> a = -0.939115566365855f; |
| vec<N> b = 0.9217841528914573f; |
| vec<N> c = -1.2845906244690837f; |
| vec<N> d = 0.295624144969963174f; |
| vec<N> f = (b*xx + a)*x; |
| vec<N> f_ = 3*b*xx + a; |
| vec<N> g = (d*xx + c)*xx + 1; |
| vec<N> g_ = (4*d*xx + 2*c)*x; |
| vec<N> gg = g*g; |
| vec<N> q = skvx::sqrt(1 - xx); |
| err_ = (f_*g - f*g_)/gg + 1/q; |
| |
| // Find d^2/dx^2(error) |
| // = ((f''g - fg'')g^2 - (f'g - fg')2gg') / g^4 + x(1 - x^2)^(-3/2) |
| // = ((f''g - fg'')g - (f'g - fg')2g') / g^3 + x(1 - x^2)^(-3/2) |
| vec<N> f__ = 6*b*x; |
| vec<N> g__ = 12*d*xx + 2*c; |
| vec<N> err__ = ((f__*g - f*g__)*g - (f_*g - f*g_)*2*g_) / (gg*g) + x/((1 - xx)*q); |
| |
| #if 0 |
| SkDebugf("\n\niter %i\n", iter); |
| #endif |
| // Ensure each lane's approximation is within maximum error. |
| for (int j = 0; j < N; ++j) { |
| #if 0 |
| SkDebugf("x=%f err=%f err'=%f err''=%f\n", |
| x[j], SkRadiansToDegrees(approx_acos_x[j] - acosf(x[j])), |
| SkRadiansToDegrees(err_[j]), SkRadiansToDegrees(err__[j])); |
| #endif |
| if (!check_approx_acos(r, x[j], approx_acos_x[j])) { |
| return; |
| } |
| } |
| |
| // Use Newton's method to update the x values to locations closer to their local minimum or |
| // maximum. (This is where d/dx(error) == 0.) |
| x -= err_/err__; |
| x = skvx::pin(x, vec<N>(-.99f), vec<N>(.99f)); |
| } |
| |
| // Ensure each lane converged to a local minimum or maximum. |
| for (int j = 0; j < N; ++j) { |
| REPORTER_ASSERT(r, SkScalarNearlyZero(err_[j])); |
| } |
| |
| // Make sure we found all the actual known locations of local min/max error. |
| for (float knownRoot : {-0.983536f, -0.867381f, -0.410923f, 0.410923f, 0.867381f, 0.983536f}) { |
| REPORTER_ASSERT(r, skvx::any(skvx::abs(x - knownRoot) < SK_ScalarNearlyZero)); |
| } |
| } |
| |
| static float precise_angle_between_vectors(SkPoint a, SkPoint b) { |
| if (a.isZero() || b.isZero()) { |
| return 0; |
| } |
| double ax=a.fX, ay=a.fY, bx=b.fX, by=b.fY; |
| double theta = (ax*bx + ay*by) / sqrt(ax*ax + ay*ay) / sqrt(bx*bx + by*by); |
| return (float)acos(theta); |
| } |
| |
| static bool check_approx_angle_between_vectors(skiatest::Reporter* r, SkVector a, SkVector b, |
| float approxTheta) { |
| float expectedTheta = precise_angle_between_vectors(a, b); |
| float error = expectedTheta - approxTheta; |
| if (!(fabsf(error) <= GRVX_FAST_ACOS_MAX_ERROR + SK_ScalarNearlyZero)) { |
| int expAx = SkFloat2Bits(a.fX) >> 23 & 0xff; |
| int expAy = SkFloat2Bits(a.fY) >> 23 & 0xff; |
| int expBx = SkFloat2Bits(b.fX) >> 23 & 0xff; |
| int expBy = SkFloat2Bits(b.fY) >> 23 & 0xff; |
| ERRORF(r, "Larger-than-expected error from grvx::approx_angle_between_vectors\n" |
| " a= {%f, %f}\n" |
| " b= {%f, %f}\n" |
| " expA= {%u, %u}\n" |
| " expB= {%u, %u}\n" |
| " approxTheta= %f (%f degrees\n" |
| " expectedTheta= %f (%f degrees)\n" |
| " error= %f (%f degrees)\n" |
| " tolerance= %f (%f degrees)\n\n", |
| a.fX, a.fY, b.fX, b.fY, expAx, expAy, expBx, expBy, approxTheta, |
| SkRadiansToDegrees(approxTheta), expectedTheta, SkRadiansToDegrees(expectedTheta), |
| error, SkRadiansToDegrees(error), GRVX_FAST_ACOS_MAX_ERROR, |
| SkRadiansToDegrees(GRVX_FAST_ACOS_MAX_ERROR)); |
| return false; |
| } |
| return true; |
| } |
| |
| static bool check_approx_angle_between_vectors(skiatest::Reporter* r, SkVector a, SkVector b) { |
| float approxTheta = grvx::approx_angle_between_vectors(bit_pun<float2>(a), |
| bit_pun<float2>(b)).val; |
| return check_approx_angle_between_vectors(r, a, b, approxTheta); |
| } |
| |
| DEF_TEST(grvx_approx_angle_between_vectors, r) { |
| // Test when a and/or b are zero. |
| REPORTER_ASSERT(r, SkScalarNearlyZero(grvx::approx_angle_between_vectors<2>({0,0}, {0,0}).val)); |
| REPORTER_ASSERT(r, SkScalarNearlyZero(grvx::approx_angle_between_vectors<2>({1,1}, {0,0}).val)); |
| REPORTER_ASSERT(r, SkScalarNearlyZero(grvx::approx_angle_between_vectors<2>({0,0}, {1,1}).val)); |
| check_approx_angle_between_vectors(r, {0,0}, {0,0}); |
| check_approx_angle_between_vectors(r, {1,1}, {0,0}); |
| check_approx_angle_between_vectors(r, {0,0}, {1,1}); |
| |
| // Test infinities. |
| REPORTER_ASSERT(r, SkScalarNearlyZero(grvx::approx_angle_between_vectors<2>( |
| {std::numeric_limits<float>::infinity(),1}, {2,3}).val)); |
| |
| // Test NaNs. |
| REPORTER_ASSERT(r, SkScalarNearlyZero(grvx::approx_angle_between_vectors<2>( |
| {std::numeric_limits<float>::quiet_NaN(),1}, {2,3}).val)); |
| |
| // Test demorms. |
| float epsilon = std::numeric_limits<float>::denorm_min(); |
| REPORTER_ASSERT(r, SkScalarNearlyZero(grvx::approx_angle_between_vectors<2>( |
| {epsilon, epsilon}, {epsilon, epsilon}).val)); |
| |
| // Test random floats of all types. |
| uint4 mantissas = {0,0,0,0}; |
| uint4 exp = uint4{126, 127, 128, 129}; |
| for (uint32_t i = 0; i < (1 << 12); ++i) { |
| // approx_angle_between_vectors is only valid for absolute values < 2^31. |
| uint4 exp_ = skvx::min(exp, 127 + 30); |
| uint32_t a=exp_[0], b=exp_[1], c=exp_[2], d=exp_[3]; |
| // approx_angle_between_vectors is only valid if at least one vector component's magnitude |
| // is >2^-31. |
| a = std::max(a, 127u - 30); |
| c = std::max(a, 127u - 30); |
| // Run two tests where both components of both vectors have the same exponent, one where |
| // both components of a given vector have the same exponent, and one where all components of |
| // all vectors have different exponents. |
| uint4 x0exp = uint4{a,c,a,a} << 23; |
| uint4 y0exp = uint4{a,c,a,b} << 23; |
| uint4 x1exp = uint4{a,c,c,c} << 23; |
| uint4 y1exp = uint4{a,c,c,d} << 23; |
| uint4 signs = uint4{i<<31, i<<30, i<<29, i<<28} & (1u<<31); |
| float4 x0 = bit_pun<float4>(signs | x0exp | mantissas[0]); |
| float4 y0 = bit_pun<float4>(signs | y0exp | mantissas[1]); |
| float4 x1 = bit_pun<float4>(signs | x1exp | mantissas[2]); |
| float4 y1 = bit_pun<float4>(signs | y1exp | mantissas[3]); |
| float4 rads = approx_angle_between_vectors(skvx::join(x0, y0), skvx::join(x1, y1)); |
| for (int j = 0; j < 4; ++j) { |
| if (!check_approx_angle_between_vectors(r, {x0[j], y0[j]}, {x1[j], y1[j]}, rads[j])) { |
| return; |
| } |
| } |
| // Adding primes makes sure we test every value before we repeat. |
| mantissas = (mantissas + uint4{123456791, 201345691, 198765433, 156789029}) & ((1<<23) - 1); |
| exp = (exp + uint4{79, 83, 199, 7}) & 0xff; |
| } |
| } |
| |
| template<int N, typename T> void check_strided_loads(skiatest::Reporter* r) { |
| using Vec = skvx::Vec<N,T>; |
| T values[N*4]; |
| std::iota(values, values + N*4, 0); |
| Vec a, b, c, d; |
| grvx::strided_load2(values, a, b); |
| for (int i = 0; i < N; ++i) { |
| REPORTER_ASSERT(r, a[i] == values[i*2]); |
| REPORTER_ASSERT(r, b[i] == values[i*2 + 1]); |
| } |
| grvx::strided_load4(values, a, b, c, d); |
| for (int i = 0; i < N; ++i) { |
| REPORTER_ASSERT(r, a[i] == values[i*4]); |
| REPORTER_ASSERT(r, b[i] == values[i*4 + 1]); |
| REPORTER_ASSERT(r, c[i] == values[i*4 + 2]); |
| REPORTER_ASSERT(r, d[i] == values[i*4 + 3]); |
| } |
| } |
| |
| template<typename T> void check_strided_loads(skiatest::Reporter* r) { |
| check_strided_loads<1,T>(r); |
| check_strided_loads<2,T>(r); |
| check_strided_loads<4,T>(r); |
| check_strided_loads<8,T>(r); |
| check_strided_loads<16,T>(r); |
| check_strided_loads<32,T>(r); |
| } |
| |
| DEF_TEST(GrVx_strided_loads, r) { |
| check_strided_loads<uint32_t>(r); |
| check_strided_loads<uint16_t>(r); |
| check_strided_loads<uint8_t>(r); |
| check_strided_loads<int32_t>(r); |
| check_strided_loads<int16_t>(r); |
| check_strided_loads<int8_t>(r); |
| check_strided_loads<float>(r); |
| } |