d461f6eb22
Bug: skia:10419 Change-Id: I050d8ed49e3a2a6d12b889961e8886f671e2d170 Reviewed-on: https://skia-review.googlesource.com/c/skia/+/337561 Reviewed-by: Brian Salomon <bsalomon@google.com> Commit-Queue: Chris Dalton <csmartdalton@google.com>
271 lines
11 KiB
C++
271 lines
11 KiB
C++
/*
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* Copyright 2020 Google Inc.
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*
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* Use of this source code is governed by a BSD-style license that can be
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* found in the LICENSE file.
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*/
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#include "include/utils/SkRandom.h"
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#include "src/core/SkGeometry.h"
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#include "src/gpu/GrVx.h"
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#include "tests/Test.h"
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#include <limits>
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#include <numeric>
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using namespace grvx;
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using skvx::bit_pun;
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DEF_TEST(grvx_cross_dot, r) {
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REPORTER_ASSERT(r, grvx::cross({0,1}, {0,1}) == 0);
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REPORTER_ASSERT(r, grvx::cross({1,0}, {1,0}) == 0);
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REPORTER_ASSERT(r, grvx::cross({1,1}, {1,1}) == 0);
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REPORTER_ASSERT(r, grvx::cross({1,1}, {1,-1}) == -2);
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REPORTER_ASSERT(r, grvx::cross({1,1}, {-1,1}) == 2);
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REPORTER_ASSERT(r, grvx::dot({0,1}, {1,0}) == 0);
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REPORTER_ASSERT(r, grvx::dot({1,0}, {0,1}) == 0);
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REPORTER_ASSERT(r, grvx::dot({1,1}, {1,-1}) == 0);
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REPORTER_ASSERT(r, grvx::dot({1,1}, {1,1}) == 2);
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REPORTER_ASSERT(r, grvx::dot({1,1}, {-1,-1}) == -2);
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SkRandom rand;
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for (int i = 0; i < 100; ++i) {
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float a=rand.nextRangeF(-1,1), b=rand.nextRangeF(-1,1), c=rand.nextRangeF(-1,1),
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d=rand.nextRangeF(-1,1);
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constexpr static float kTolerance = 1.f / (1 << 20);
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REPORTER_ASSERT(r, SkScalarNearlyEqual(
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grvx::cross({a,b}, {c,d}), SkPoint::CrossProduct({a,b}, {c,d}), kTolerance));
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REPORTER_ASSERT(r, SkScalarNearlyEqual(
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grvx::dot({a,b}, {c,d}), SkPoint::DotProduct({a,b}, {c,d}), kTolerance));
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}
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}
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static bool check_approx_acos(skiatest::Reporter* r, float x, float approx_acos_x) {
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float acosf_x = acosf(x);
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float error = acosf_x - approx_acos_x;
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if (!(fabsf(error) <= GRVX_FAST_ACOS_MAX_ERROR)) {
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ERRORF(r, "Larger-than-expected error from grvx::approx_acos\n"
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" x= %f\n"
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" approx_acos_x= %f (%f degrees\n"
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" acosf_x= %f (%f degrees\n"
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" error= %f (%f degrees)\n"
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" tolerance= %f (%f degrees)\n\n",
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x, approx_acos_x, SkRadiansToDegrees(approx_acos_x), acosf_x,
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SkRadiansToDegrees(acosf_x), error, SkRadiansToDegrees(error),
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GRVX_FAST_ACOS_MAX_ERROR, SkRadiansToDegrees(GRVX_FAST_ACOS_MAX_ERROR));
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return false;
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}
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return true;
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}
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DEF_TEST(grvx_approx_acos, r) {
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float4 boundaries = approx_acos(float4{-1, 0, 1, 0});
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check_approx_acos(r, -1, boundaries[0]);
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check_approx_acos(r, 0, boundaries[1]);
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check_approx_acos(r, +1, boundaries[2]);
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// Select a distribution of starting points around which to begin testing approx_acos. These
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// fall roughly around the known minimum and maximum errors. No need to include -1, 0, or 1
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// since those were just tested above. (Those are tricky because 0 is an inflection and the
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// derivative is infinite at 1 and -1.)
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constexpr static int N = 8;
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vec<8> x = {-.99f, -.8f, -.4f, -.2f, .2f, .4f, .8f, .99f};
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// Converge at the various local minima and maxima of "approx_acos(x) - cosf(x)" and verify that
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// approx_acos is always within "kTolerance" degrees of the expected answer.
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vec<N> err_;
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for (int iter = 0; iter < 10; ++iter) {
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// Run our approximate inverse cosine approximation.
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vec<N> approx_acos_x = approx_acos(x);
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// Find d/dx(error)
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// = d/dx(approx_acos(x) - acos(x))
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// = (f'g - fg')/gg + 1/sqrt(1 - x^2), [where f = bx^3 + ax, g = dx^4 + cx^2 + 1]
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vec<N> xx = x*x;
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vec<N> a = -0.939115566365855f;
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vec<N> b = 0.9217841528914573f;
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vec<N> c = -1.2845906244690837f;
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vec<N> d = 0.295624144969963174f;
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vec<N> f = (b*xx + a)*x;
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vec<N> f_ = 3*b*xx + a;
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vec<N> g = (d*xx + c)*xx + 1;
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vec<N> g_ = (4*d*xx + 2*c)*x;
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vec<N> gg = g*g;
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vec<N> q = skvx::sqrt(1 - xx);
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err_ = (f_*g - f*g_)/gg + 1/q;
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// Find d^2/dx^2(error)
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// = ((f''g - fg'')g^2 - (f'g - fg')2gg') / g^4 + x(1 - x^2)^(-3/2)
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// = ((f''g - fg'')g - (f'g - fg')2g') / g^3 + x(1 - x^2)^(-3/2)
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vec<N> f__ = 6*b*x;
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vec<N> g__ = 12*d*xx + 2*c;
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vec<N> err__ = ((f__*g - f*g__)*g - (f_*g - f*g_)*2*g_) / (gg*g) + x/((1 - xx)*q);
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#if 0
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SkDebugf("\n\niter %i\n", iter);
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#endif
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// Ensure each lane's approximation is within maximum error.
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for (int j = 0; j < N; ++j) {
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#if 0
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SkDebugf("x=%f err=%f err'=%f err''=%f\n",
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x[j], SkRadiansToDegrees(approx_acos_x[j] - acosf(x[j])),
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SkRadiansToDegrees(err_[j]), SkRadiansToDegrees(err__[j]));
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#endif
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if (!check_approx_acos(r, x[j], approx_acos_x[j])) {
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return;
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}
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}
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// Use Newton's method to update the x values to locations closer to their local minimum or
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// maximum. (This is where d/dx(error) == 0.)
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x -= err_/err__;
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x = skvx::pin(x, vec<N>(-.99f), vec<N>(.99f));
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}
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// Ensure each lane converged to a local minimum or maximum.
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for (int j = 0; j < N; ++j) {
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REPORTER_ASSERT(r, SkScalarNearlyZero(err_[j]));
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}
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// Make sure we found all the actual known locations of local min/max error.
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for (float knownRoot : {-0.983536f, -0.867381f, -0.410923f, 0.410923f, 0.867381f, 0.983536f}) {
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REPORTER_ASSERT(r, skvx::any(skvx::abs(x - knownRoot) < SK_ScalarNearlyZero));
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}
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}
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static float precise_angle_between_vectors(SkPoint a, SkPoint b) {
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if (a.isZero() || b.isZero()) {
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return 0;
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}
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double ax=a.fX, ay=a.fY, bx=b.fX, by=b.fY;
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double theta = (ax*bx + ay*by) / sqrt(ax*ax + ay*ay) / sqrt(bx*bx + by*by);
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return (float)acos(theta);
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}
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static bool check_approx_angle_between_vectors(skiatest::Reporter* r, SkVector a, SkVector b,
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float approxTheta) {
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float expectedTheta = precise_angle_between_vectors(a, b);
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float error = expectedTheta - approxTheta;
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if (!(fabsf(error) <= GRVX_FAST_ACOS_MAX_ERROR + SK_ScalarNearlyZero)) {
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int expAx = SkFloat2Bits(a.fX) >> 23 & 0xff;
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int expAy = SkFloat2Bits(a.fY) >> 23 & 0xff;
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int expBx = SkFloat2Bits(b.fX) >> 23 & 0xff;
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int expBy = SkFloat2Bits(b.fY) >> 23 & 0xff;
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ERRORF(r, "Larger-than-expected error from grvx::approx_angle_between_vectors\n"
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" a= {%f, %f}\n"
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" b= {%f, %f}\n"
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" expA= {%u, %u}\n"
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" expB= {%u, %u}\n"
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" approxTheta= %f (%f degrees\n"
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" expectedTheta= %f (%f degrees)\n"
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" error= %f (%f degrees)\n"
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" tolerance= %f (%f degrees)\n\n",
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a.fX, a.fY, b.fX, b.fY, expAx, expAy, expBx, expBy, approxTheta,
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SkRadiansToDegrees(approxTheta), expectedTheta, SkRadiansToDegrees(expectedTheta),
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error, SkRadiansToDegrees(error), GRVX_FAST_ACOS_MAX_ERROR,
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SkRadiansToDegrees(GRVX_FAST_ACOS_MAX_ERROR));
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return false;
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}
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return true;
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}
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static bool check_approx_angle_between_vectors(skiatest::Reporter* r, SkVector a, SkVector b) {
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float approxTheta = grvx::approx_angle_between_vectors<1>(a.fX, a.fY, b.fX, b.fY).val;
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return check_approx_angle_between_vectors(r, a, b, approxTheta);
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}
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DEF_TEST(grvx_approx_angle_between_vectors, r) {
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// Test when a and/or b are zero.
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REPORTER_ASSERT(r, SkScalarNearlyZero(grvx::approx_angle_between_vectors<1>(0,0,0,0).val));
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REPORTER_ASSERT(r, SkScalarNearlyZero(grvx::approx_angle_between_vectors<1>(1,1,0,0).val));
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REPORTER_ASSERT(r, SkScalarNearlyZero(grvx::approx_angle_between_vectors<1>(0,0,1,1).val));
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check_approx_angle_between_vectors(r, {0,0}, {0,0});
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check_approx_angle_between_vectors(r, {1,1}, {0,0});
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check_approx_angle_between_vectors(r, {0,0}, {1,1});
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// Test infinities.
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REPORTER_ASSERT(r, SkScalarNearlyZero(grvx::approx_angle_between_vectors<1>(
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std::numeric_limits<float>::infinity(),1,2,3).val));
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// Test NaNs.
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REPORTER_ASSERT(r, SkScalarNearlyZero(grvx::approx_angle_between_vectors<1>(
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std::numeric_limits<float>::quiet_NaN(),1,2,3).val));
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// Test demorms.
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float epsilon = std::numeric_limits<float>::denorm_min();
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REPORTER_ASSERT(r, SkScalarNearlyZero(grvx::approx_angle_between_vectors<1>(
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epsilon, epsilon, epsilon, epsilon).val));
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// Test random floats of all types.
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uint4 mantissas = {0,0,0,0};
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uint4 exp = uint4{126, 127, 128, 129};
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for (uint32_t i = 0; i < (1 << 12); ++i) {
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// approx_angle_between_vectors is only valid for absolute values < 2^31.
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uint4 exp_ = skvx::min(exp, 127 + 30);
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uint32_t a=exp_[0], b=exp_[1], c=exp_[2], d=exp_[3];
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// approx_angle_between_vectors is only valid if at least one vector component's magnitude
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// is >2^-31.
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a = std::max(a, 127u - 30);
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c = std::max(a, 127u - 30);
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// Run two tests where both components of both vectors have the same exponent, one where
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// both components of a given vector have the same exponent, and one where all components of
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// all vectors have different exponents.
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uint4 x0exp = uint4{a,c,a,a} << 23;
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uint4 y0exp = uint4{a,c,a,b} << 23;
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uint4 x1exp = uint4{a,c,c,c} << 23;
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uint4 y1exp = uint4{a,c,c,d} << 23;
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uint4 signs = uint4{i<<31, i<<30, i<<29, i<<28} & (1u<<31);
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float4 x0 = bit_pun<float4>(signs | x0exp | mantissas[0]);
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float4 y0 = bit_pun<float4>(signs | y0exp | mantissas[1]);
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float4 x1 = bit_pun<float4>(signs | x1exp | mantissas[2]);
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float4 y1 = bit_pun<float4>(signs | y1exp | mantissas[3]);
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float4 rads = approx_angle_between_vectors(x0, y0, x1, y1);
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for (int j = 0; j < 4; ++j) {
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if (!check_approx_angle_between_vectors(r, {x0[j], y0[j]}, {x1[j], y1[j]}, rads[j])) {
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return;
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}
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}
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// Adding primes makes sure we test every value before we repeat.
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mantissas = (mantissas + uint4{123456791, 201345691, 198765433, 156789029}) & ((1<<23) - 1);
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exp = (exp + uint4{79, 83, 199, 7}) & 0xff;
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}
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}
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template<int N, typename T> void check_strided_loads(skiatest::Reporter* r) {
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using Vec = skvx::Vec<N,T>;
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T values[N*4];
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std::iota(values, values + N*4, 0);
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Vec a, b, c, d;
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grvx::strided_load2(values, a, b);
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for (int i = 0; i < N; ++i) {
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REPORTER_ASSERT(r, a[i] == values[i*2]);
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REPORTER_ASSERT(r, b[i] == values[i*2 + 1]);
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}
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grvx::strided_load4(values, a, b, c, d);
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for (int i = 0; i < N; ++i) {
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REPORTER_ASSERT(r, a[i] == values[i*4]);
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REPORTER_ASSERT(r, b[i] == values[i*4 + 1]);
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REPORTER_ASSERT(r, c[i] == values[i*4 + 2]);
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REPORTER_ASSERT(r, d[i] == values[i*4 + 3]);
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}
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}
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template<typename T> void check_strided_loads(skiatest::Reporter* r) {
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check_strided_loads<1,T>(r);
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check_strided_loads<2,T>(r);
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check_strided_loads<4,T>(r);
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check_strided_loads<8,T>(r);
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check_strided_loads<16,T>(r);
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check_strided_loads<32,T>(r);
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}
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DEF_TEST(GrVx_strided_loads, r) {
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check_strided_loads<uint32_t>(r);
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check_strided_loads<uint16_t>(r);
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check_strided_loads<uint8_t>(r);
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check_strided_loads<int32_t>(r);
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check_strided_loads<int16_t>(r);
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check_strided_loads<int8_t>(r);
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check_strided_loads<float>(r);
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}
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