Refactor jet_tests.cc
1. Break tests for one function into its own TEST instance.
2. Use a gmock matcher which gives better logging, previously
we were using a function which in turn used another function
in test_utils. It made tracking down the failing test very
hard.
3. Disable a hypot3 underflow and overflow test when using
libc++ as the three argument in libc++ is borked.
4. The use of the matcher has made a number of comments redundant
so I have removed them.
This is the first step in cleaning up these tests and then expanding
them.
Change-Id: Ib0c827f44432e2496e50b8cda3e06c26bdf50f08
diff --git a/internal/ceres/jet_test.cc b/internal/ceres/jet_test.cc
index 7946908..e613b3f 100644
--- a/internal/ceres/jet_test.cc
+++ b/internal/ceres/jet_test.cc
@@ -37,18 +37,17 @@
#include "ceres/stringprintf.h"
#include "ceres/test_util.h"
#include "glog/logging.h"
+#include "gmock/gmock.h"
#include "gtest/gtest.h"
-#define VL VLOG(1)
-
namespace ceres {
namespace internal {
namespace {
-const double kE = 2.71828182845904523536;
+constexpr double kE = 2.71828182845904523536;
-typedef Jet<double, 2> J;
+using J = Jet<double, 2>;
// Convenient shorthand for making a jet.
J MakeJet(double a, double v0, double v1) {
@@ -59,13 +58,37 @@
return z;
}
-// On a 32-bit optimized build, the mismatch is about 1.4e-14.
double const kTolerance = 1e-13;
-void ExpectJetsClose(const J& x, const J& y) {
- ExpectClose(x.a, y.a, kTolerance);
- ExpectClose(x.v[0], y.v[0], kTolerance);
- ExpectClose(x.v[1], y.v[1], kTolerance);
+bool AreAlmostEqual(double x, double y, double max_abs_relative_difference) {
+ if (std::isnan(x) && std::isnan(y)) {
+ return true;
+ }
+
+ if (std::isinf(x) && std::isinf(y)) {
+ return (std::signbit(x) == std::signbit(y));
+ }
+
+ double absolute_difference = std::abs(x - y);
+ double relative_difference =
+ absolute_difference / std::max(std::abs(x), std::abs(y));
+
+ if (x == 0 || y == 0) {
+ // If x or y is exactly zero, then relative difference doesn't have any
+ // meaning. Take the absolute difference instead.
+ relative_difference = absolute_difference;
+ }
+ return relative_difference <= max_abs_relative_difference;
+}
+
+MATCHER_P(IsAlmostEqualTo, y, "") {
+ const bool result = (AreAlmostEqual(arg.a, y.a, kTolerance) &&
+ AreAlmostEqual(arg.v[0], y.v[0], kTolerance) &&
+ AreAlmostEqual(arg.v[1], y.v[1], kTolerance));
+ if (!result) {
+ *result_listener << "\nexpected - actual : " << y - arg;
+ }
+ return result;
}
const double kStep = 1e-8;
@@ -77,8 +100,8 @@
const double exact_dx = f(MakeJet(x, 1.0, 0.0)).v[0];
const double estimated_dx =
(f(J(x + kStep)).a - f(J(x - kStep)).a) / (2.0 * kStep);
- VL << name << "(" << x << "), exact dx: " << exact_dx
- << ", estimated dx: " << estimated_dx;
+ VLOG(1) << name << "(" << x << "), exact dx: " << exact_dx
+ << ", estimated dx: " << estimated_dx;
ExpectClose(exact_dx, estimated_dx, kNumericalTolerance);
}
@@ -102,504 +125,182 @@
(f(J(x + kStep), J(y)).a - f(J(x - kStep), J(y)).a) / (2.0 * kStep);
const double estimated_dy =
(f(J(x), J(y + kStep)).a - f(J(x), J(y - kStep)).a) / (2.0 * kStep);
- VL << name << "(" << x << ", " << y << "), exact dx: " << exact_dx
- << ", estimated dx: " << estimated_dx;
+ VLOG(1) << name << "(" << x << ", " << y << "), exact dx: " << exact_dx
+ << ", estimated dx: " << estimated_dx;
ExpectClose(exact_dx, estimated_dx, kNumericalTolerance);
- VL << name << "(" << x << ", " << y << "), exact dy: " << exact_dy
- << ", estimated dy: " << estimated_dy;
+ VLOG(1) << name << "(" << x << ", " << y << "), exact dy: " << exact_dy
+ << ", estimated dy: " << estimated_dy;
ExpectClose(exact_dy, estimated_dy, kNumericalTolerance);
}
} // namespace
-TEST(Jet, Jet) {
- // Pick arbitrary values for x and y.
- J x = MakeJet(2.3, -2.7, 1e-3);
- J y = MakeJet(1.7, 0.5, 1e+2);
- J z = MakeJet(1e-6, 1e-4, 1e-2);
+// Pick arbitrary values for x and y.
+const J x = MakeJet(2.3, -2.7, 1e-3);
+const J y = MakeJet(1.7, 0.5, 1e+2);
+const J z = MakeJet(1e-6, 1e-4, 1e-2);
- VL << "x = " << x;
- VL << "y = " << y;
- VL << "z = " << z;
-
- { // Check that log(exp(x)) == x.
- J z = exp(x);
- J w = log(z);
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(w, x);
- }
-
- { // Check that expm1(log1p(x)) == x.
- J z = expm1(x);
- J w = log1p(z);
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(w, x);
- }
-
- { // Check that log1p(expm1(x)) == x.
- J z = log1p(x);
- J w = expm1(z);
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(w, x);
- }
-
- { // Check that (x * y) / x == y.
- J z = x * y;
- J w = z / x;
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(w, y);
- }
-
- { // Check that sqrt(x * x) == x.
- J z = x * x;
- J w = sqrt(z);
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(w, x);
- }
-
- { // Check that sqrt(y) * sqrt(y) == y.
- J z = sqrt(y);
- J w = z * z;
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(w, y);
- }
+TEST(Jet, Elementary) {
+ EXPECT_THAT((x * y) / x, IsAlmostEqualTo(y));
+ EXPECT_THAT(sqrt(x * x), IsAlmostEqualTo(x));
+ EXPECT_THAT(sqrt(y) * sqrt(y), IsAlmostEqualTo(y));
NumericalTest("sqrt", sqrt<double, 2>, 0.00001);
NumericalTest("sqrt", sqrt<double, 2>, 1.0);
- { // Check that cos(2*x) = cos(x)^2 - sin(x)^2
- J z = cos(J(2.0) * x);
- J w = cos(x) * cos(x) - sin(x) * sin(x);
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(w, z);
- }
-
- { // Check that sin(2*x) = 2*cos(x)*sin(x)
- J z = sin(J(2.0) * x);
- J w = J(2.0) * cos(x) * sin(x);
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(w, z);
- }
-
- { // Check that cos(x)*cos(x) + sin(x)*sin(x) = 1
- J z = cos(x) * cos(x);
- J w = sin(x) * sin(x);
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(z + w, J(1.0));
- }
-
- { // Check that atan2(r*sin(t), r*cos(t)) = t.
- J t = MakeJet(0.7, -0.3, +1.5);
- J r = MakeJet(2.3, 0.13, -2.4);
- VL << "t = " << t;
- VL << "r = " << r;
-
- J u = atan2(r * sin(t), r * cos(t));
- VL << "u = " << u;
-
- ExpectJetsClose(u, t);
- }
-
- { // Check that tan(x) = sin(x) / cos(x).
- J z = tan(x);
- J w = sin(x) / cos(x);
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(z, w);
- }
-
- { // Check that tan(atan(x)) = x.
- J z = tan(atan(x));
- J w = x;
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(z, w);
- }
-
- { // Check that cosh(x)*cosh(x) - sinh(x)*sinh(x) = 1
- J z = cosh(x) * cosh(x);
- J w = sinh(x) * sinh(x);
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(z - w, J(1.0));
- }
-
- { // Check that tanh(x + y) = (tanh(x) + tanh(y)) / (1 + tanh(x) tanh(y))
- J z = tanh(x + y);
- J w = (tanh(x) + tanh(y)) / (J(1.0) + tanh(x) * tanh(y));
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(z, w);
- }
-
- { // Check that pow(x, 1) == x.
- VL << "x = " << x;
-
- J u = pow(x, 1.);
- VL << "u = " << u;
-
- ExpectJetsClose(x, u);
- }
-
- { // Check that pow(x, 1) == x.
- J y = MakeJet(1, 0.0, 0.0);
- VL << "x = " << x;
- VL << "y = " << y;
-
- J u = pow(x, y);
- VL << "u = " << u;
-
- ExpectJetsClose(x, u);
- }
-
- { // Check that pow(e, log(x)) == x.
- J logx = log(x);
-
- VL << "x = " << x;
- VL << "y = " << y;
-
- J u = pow(kE, logx);
- VL << "u = " << u;
-
- ExpectJetsClose(x, u);
- }
-
- { // Check that pow(e, log(x)) == x.
- J logx = log(x);
- J e = MakeJet(kE, 0., 0.);
- VL << "x = " << x;
- VL << "log(x) = " << logx;
-
- J u = pow(e, logx);
- VL << "u = " << u;
-
- ExpectJetsClose(x, u);
- }
-
- { // Check that pow(e, log(x)) == x.
- J logx = log(x);
- J e = MakeJet(kE, 0., 0.);
- VL << "x = " << x;
- VL << "logx = " << logx;
-
- J u = pow(e, logx);
- VL << "u = " << u;
-
- ExpectJetsClose(x, u);
- }
-
- { // Check that pow(x,y) = exp(y*log(x)).
- J logx = log(x);
- J e = MakeJet(kE, 0., 0.);
- VL << "x = " << x;
- VL << "logx = " << logx;
-
- J u = pow(e, y * logx);
- J v = pow(x, y);
- VL << "u = " << u;
- VL << "v = " << v;
-
- ExpectJetsClose(v, u);
- }
-
- { // Check that pow(0, y) == 0 for y > 1, with both arguments Jets.
- // This tests special case handling inside pow().
- J a = MakeJet(0, 1, 2);
- J b = MakeJet(2, 3, 4);
- VL << "a = " << a;
- VL << "b = " << b;
-
- J c = pow(a, b);
- VL << "a^b = " << c;
- ExpectJetsClose(c, MakeJet(0, 0, 0));
- }
-
- { // Check that pow(0, y) == 0 for y == 1, with both arguments Jets.
- // This tests special case handling inside pow().
- J a = MakeJet(0, 1, 2);
- J b = MakeJet(1, 3, 4);
- VL << "a = " << a;
- VL << "b = " << b;
-
- J c = pow(a, b);
- VL << "a^b = " << c;
- ExpectJetsClose(c, MakeJet(0, 1, 2));
- }
-
- { // Check that pow(0, <1) is not finite, with both arguments Jets.
- for (int i = 1; i < 10; i++) {
- J a = MakeJet(0, 1, 2);
- J b = MakeJet(i * 0.1, 3, 4); // b = 0.1 ... 0.9
- VL << "a = " << a;
- VL << "b = " << b;
-
- J c = pow(a, b);
- VL << "a^b = " << c;
- EXPECT_EQ(c.a, 0.0);
- EXPECT_FALSE(IsFinite(c.v[0]));
- EXPECT_FALSE(IsFinite(c.v[1]));
- }
- for (int i = -10; i < 0; i++) {
- J a = MakeJet(0, 1, 2);
- J b = MakeJet(i * 0.1, 3, 4); // b = -1,-0.9 ... -0.1
- VL << "a = " << a;
- VL << "b = " << b;
-
- J c = pow(a, b);
- VL << "a^b = " << c;
- EXPECT_FALSE(IsFinite(c.a));
- EXPECT_FALSE(IsFinite(c.v[0]));
- EXPECT_FALSE(IsFinite(c.v[1]));
- }
-
- {
- // The special case of 0^0 = 1 defined by the C standard.
- J a = MakeJet(0, 1, 2);
- J b = MakeJet(0, 3, 4);
- VL << "a = " << a;
- VL << "b = " << b;
-
- J c = pow(a, b);
- VL << "a^b = " << c;
- EXPECT_EQ(c.a, 1.0);
- EXPECT_FALSE(IsFinite(c.v[0]));
- EXPECT_FALSE(IsFinite(c.v[1]));
- }
- }
-
- { // Check that pow(<0, b) is correct for integer b.
- // This tests special case handling inside pow().
- J a = MakeJet(-1.5, 3, 4);
-
- // b integer:
- for (int i = -10; i <= 10; i++) {
- J b = MakeJet(i, 0, 5);
- VL << "a = " << a;
- VL << "b = " << b;
-
- J c = pow(a, b);
- VL << "a^b = " << c;
- ExpectClose(c.a, pow(-1.5, i), kTolerance);
- EXPECT_TRUE(IsFinite(c.v[0]));
- EXPECT_FALSE(IsFinite(c.v[1]));
- ExpectClose(c.v[0], i * pow(-1.5, i - 1) * 3.0, kTolerance);
- }
- }
-
- { // Check that pow(<0, b) is correct for noninteger b.
- // This tests special case handling inside pow().
- J a = MakeJet(-1.5, 3, 4);
- J b = MakeJet(-2.5, 0, 5);
- VL << "a = " << a;
- VL << "b = " << b;
-
- J c = pow(a, b);
- VL << "a^b = " << c;
- EXPECT_FALSE(IsFinite(c.a));
- EXPECT_FALSE(IsFinite(c.v[0]));
- EXPECT_FALSE(IsFinite(c.v[1]));
- }
-
+ EXPECT_THAT(x + 1.0, IsAlmostEqualTo(1.0 + x));
{
- // Check that pow(0,y) == 0 for y == 2, with the second argument a
- // Jet. This tests special case handling inside pow().
- double a = 0;
- J b = MakeJet(2, 3, 4);
- VL << "a = " << a;
- VL << "b = " << b;
-
- J c = pow(a, b);
- VL << "a^b = " << c;
- ExpectJetsClose(c, MakeJet(0, 0, 0));
- }
-
- {
- // Check that pow(<0,y) is correct for integer y. This tests special case
- // handling inside pow().
- double a = -1.5;
- for (int i = -10; i <= 10; i++) {
- J b = MakeJet(i, 3, 0);
- VL << "a = " << a;
- VL << "b = " << b;
-
- J c = pow(a, b);
- VL << "a^b = " << c;
- ExpectClose(c.a, pow(-1.5, i), kTolerance);
- EXPECT_FALSE(IsFinite(c.v[0]));
- EXPECT_TRUE(IsFinite(c.v[1]));
- ExpectClose(c.v[1], 0, kTolerance);
- }
- }
-
- {
- // Check that pow(<0,y) is correct for noninteger y. This tests special
- // case handling inside pow().
- double a = -1.5;
- J b = MakeJet(-3.14, 3, 0);
- VL << "a = " << a;
- VL << "b = " << b;
-
- J c = pow(a, b);
- VL << "a^b = " << c;
- EXPECT_FALSE(IsFinite(c.a));
- EXPECT_FALSE(IsFinite(c.v[0]));
- EXPECT_FALSE(IsFinite(c.v[1]));
- }
-
- { // Check that 1 + x == x + 1.
- J a = x + 1.0;
- J b = 1.0 + x;
J c = x;
c += 1.0;
-
- ExpectJetsClose(a, b);
- ExpectJetsClose(a, c);
+ EXPECT_THAT(c, IsAlmostEqualTo(1.0 + x));
}
- { // Check that 1 - x == -(x - 1).
- J a = 1.0 - x;
- J b = -(x - 1.0);
+ EXPECT_THAT(-(x - 1.0), IsAlmostEqualTo(1.0 - x));
+ {
J c = x;
c -= 1.0;
-
- ExpectJetsClose(a, b);
- ExpectJetsClose(a, -c);
+ EXPECT_THAT(c, IsAlmostEqualTo(x - 1.0));
}
- { // Check that (x/s)*s == (x*s)/s.
- J a = x / 5.0;
- J b = x * 5.0;
+ EXPECT_THAT((x * 5.0) / 5.0, IsAlmostEqualTo((x / 5.0) * 5.0));
+ EXPECT_THAT((x * 5.0) / 5.0, IsAlmostEqualTo(x));
+ EXPECT_THAT((x / 5.0) * 5.0, IsAlmostEqualTo(x));
+
+ {
J c = x;
c /= 5.0;
J d = x;
d *= 5.0;
-
- ExpectJetsClose(5.0 * a, b / 5.0);
- ExpectJetsClose(a, c);
- ExpectJetsClose(b, d);
+ EXPECT_THAT(c, IsAlmostEqualTo(x / 5.0));
+ EXPECT_THAT(d, IsAlmostEqualTo(5.0 * x));
}
- { // Check that x / y == 1 / (y / x).
- J a = x / y;
- J b = 1.0 / (y / x);
- VL << "a = " << a;
- VL << "b = " << b;
+ EXPECT_THAT(1.0 / (y / x), IsAlmostEqualTo(x / y));
+}
- ExpectJetsClose(a, b);
+TEST(Jet, Trigonometric) {
+ EXPECT_THAT(cos(2.0 * x), IsAlmostEqualTo(cos(x) * cos(x) - sin(x) * sin(x)));
+ EXPECT_THAT(sin(2.0 * x), IsAlmostEqualTo(2.0 * sin(x) * cos(x)));
+ EXPECT_THAT(sin(x) * sin(x) + cos(x) * cos(x), IsAlmostEqualTo(J(1.0)));
+
+ {
+ J t = MakeJet(0.7, -0.3, +1.5);
+ J r = MakeJet(2.3, 0.13, -2.4);
+ EXPECT_THAT(atan2(r * sin(t), r * cos(t)), IsAlmostEqualTo(t));
}
- { // Check that abs(-x * x) == x * x.
- ExpectJetsClose(abs(-x * x), x * x);
- // Check that abs(-x) == sqrt(x * x).
- ExpectJetsClose(abs(-x), sqrt(x * x));
+ EXPECT_THAT(sin(x) / cos(x), IsAlmostEqualTo(tan(x)));
+ EXPECT_THAT(tan(atan(x)), IsAlmostEqualTo(x));
+
+ {
+ J a = MakeJet(0.1, -2.7, 1e-3);
+ EXPECT_THAT(cos(acos(a)), IsAlmostEqualTo(a));
+ EXPECT_THAT(acos(cos(a)), IsAlmostEqualTo(a));
+
+ J b = MakeJet(0.6, 0.5, 1e+2);
+ EXPECT_THAT(cos(acos(b)), IsAlmostEqualTo(b));
+ EXPECT_THAT(acos(cos(b)), IsAlmostEqualTo(b));
}
+
+ {
+ J a = MakeJet(0.1, -2.7, 1e-3);
+ EXPECT_THAT(sin(asin(a)), IsAlmostEqualTo(a));
+ EXPECT_THAT(asin(sin(a)), IsAlmostEqualTo(a));
+
+ J b = MakeJet(0.4, 0.5, 1e+2);
+ EXPECT_THAT(sin(asin(b)), IsAlmostEqualTo(b));
+ EXPECT_THAT(asin(sin(b)), IsAlmostEqualTo(b));
+ }
+}
+
+TEST(Jet, Hyperbolic) {
+ // cosh(x)*cosh(x) - sinh(x)*sinh(x) = 1
+ EXPECT_THAT(cosh(x) * cosh(x) - sinh(x) * sinh(x), IsAlmostEqualTo(J(1.0)));
+
+ // tanh(x + y) = (tanh(x) + tanh(y)) / (1 + tanh(x) tanh(y))
+ EXPECT_THAT(
+ tanh(x + y),
+ IsAlmostEqualTo((tanh(x) + tanh(y)) / (J(1.0) + tanh(x) * tanh(y))));
+}
+
+TEST(Jet, Abs) {
+ EXPECT_THAT(abs(-x * x), IsAlmostEqualTo(x * x));
+ EXPECT_THAT(abs(-x), IsAlmostEqualTo(sqrt(x * x)));
+
{
J a = MakeJet(-std::numeric_limits<double>::quiet_NaN(), 2.0, 4.0);
J b = abs(a);
EXPECT_TRUE(std::signbit(b.v[0]));
EXPECT_TRUE(std::signbit(b.v[1]));
}
+}
- { // Check that cos(acos(x)) == x.
- J a = MakeJet(0.1, -2.7, 1e-3);
- ExpectJetsClose(cos(acos(a)), a);
- ExpectJetsClose(acos(cos(a)), a);
+TEST(Jet, Bessel) {
+ J zero = J(0.0);
- J b = MakeJet(0.6, 0.5, 1e+2);
- ExpectJetsClose(cos(acos(b)), b);
- ExpectJetsClose(acos(cos(b)), b);
- }
+ EXPECT_THAT(BesselJ0(zero), IsAlmostEqualTo(J(1.0)));
+ EXPECT_THAT(BesselJ1(zero), IsAlmostEqualTo(zero));
+ EXPECT_THAT(BesselJn(2, zero), IsAlmostEqualTo(zero));
+ EXPECT_THAT(BesselJn(3, zero), IsAlmostEqualTo(zero));
- { // Check that sin(asin(x)) == x.
- J a = MakeJet(0.1, -2.7, 1e-3);
- ExpectJetsClose(sin(asin(a)), a);
- ExpectJetsClose(asin(sin(a)), a);
+ J z = MakeJet(0.1, -2.7, 1e-3);
- J b = MakeJet(0.4, 0.5, 1e+2);
- ExpectJetsClose(sin(asin(b)), b);
- ExpectJetsClose(asin(sin(b)), b);
- }
+ EXPECT_THAT(BesselJ0(z), IsAlmostEqualTo(BesselJn(0, z)));
+ EXPECT_THAT(BesselJ1(z), IsAlmostEqualTo(BesselJn(1, z)));
- {
- J zero = J(0.0);
+ // See formula http://dlmf.nist.gov/10.6.E1
+ EXPECT_THAT(BesselJ0(z) + BesselJn(2, z),
+ IsAlmostEqualTo((2.0 / z) * BesselJ1(z)));
+}
- // Check that J0(0) == 1.
- ExpectJetsClose(BesselJ0(zero), J(1.0));
-
- // Check that J1(0) == 0.
- ExpectJetsClose(BesselJ1(zero), zero);
-
- // Check that J2(0) == 0.
- ExpectJetsClose(BesselJn(2, zero), zero);
-
- // Check that J3(0) == 0.
- ExpectJetsClose(BesselJn(3, zero), zero);
-
- J z = MakeJet(0.1, -2.7, 1e-3);
-
- // Check that J0(z) == Jn(0,z).
- ExpectJetsClose(BesselJ0(z), BesselJn(0, z));
-
- // Check that J1(z) == Jn(1,z).
- ExpectJetsClose(BesselJ1(z), BesselJn(1, z));
-
- // Check that J0(z)+J2(z) == (2/z)*J1(z).
- // See formula http://dlmf.nist.gov/10.6.E1
- ExpectJetsClose(BesselJ0(z) + BesselJn(2, z), (2.0 / z) * BesselJ1(z));
- }
-
- { // Check that floor of a positive number works.
+TEST(Jet, Floor) {
+ { // floor of a positive number works.
J a = MakeJet(0.1, -2.7, 1e-3);
J b = floor(a);
J expected = MakeJet(floor(a.a), 0.0, 0.0);
EXPECT_EQ(expected, b);
}
- { // Check that floor of a negative number works.
+ { // floor of a negative number works.
J a = MakeJet(-1.1, -2.7, 1e-3);
J b = floor(a);
J expected = MakeJet(floor(a.a), 0.0, 0.0);
EXPECT_EQ(expected, b);
}
- { // Check that floor of a positive number works.
+ { // floor of a positive number works.
J a = MakeJet(10.123, -2.7, 1e-3);
J b = floor(a);
J expected = MakeJet(floor(a.a), 0.0, 0.0);
EXPECT_EQ(expected, b);
}
+}
- { // Check that ceil of a positive number works.
+TEST(Jet, Ceil) {
+ { // ceil of a positive number works.
J a = MakeJet(0.1, -2.7, 1e-3);
J b = ceil(a);
J expected = MakeJet(ceil(a.a), 0.0, 0.0);
EXPECT_EQ(expected, b);
}
- { // Check that ceil of a negative number works.
+ { // ceil of a negative number works.
J a = MakeJet(-1.1, -2.7, 1e-3);
J b = ceil(a);
J expected = MakeJet(ceil(a.a), 0.0, 0.0);
EXPECT_EQ(expected, b);
}
- { // Check that ceil of a positive number works.
+ { // ceil of a positive number works.
J a = MakeJet(10.123, -2.7, 1e-3);
J b = ceil(a);
J expected = MakeJet(ceil(a.a), 0.0, 0.0);
EXPECT_EQ(expected, b);
}
+}
- { // Check that erf works.
+TEST(Jet, Erf) {
+ { // erf works.
J a = MakeJet(10.123, -2.7, 1e-3);
J b = erf(a);
J expected = MakeJet(erf(a.a), 0.0, 0.0);
@@ -609,8 +310,10 @@
NumericalTest("erf", erf<double, 2>, 1e-5);
NumericalTest("erf", erf<double, 2>, 0.5);
NumericalTest("erf", erf<double, 2>, 100.0);
+}
- { // Check that erfc works.
+TEST(Jet, Erfc) {
+ { // erfc works.
J a = MakeJet(10.123, -2.7, 1e-3);
J b = erfc(a);
J expected = MakeJet(erfc(a.a), 0.0, 0.0);
@@ -620,82 +323,48 @@
NumericalTest("erfc", erfc<double, 2>, 1e-5);
NumericalTest("erfc", erfc<double, 2>, 0.5);
NumericalTest("erfc", erfc<double, 2>, 100.0);
+}
- { // Check that cbrt(x * x * x) == x.
- J z = x * x * x;
- J w = cbrt(z);
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(w, x);
- }
+TEST(Jet, Cbrt) {
+ EXPECT_THAT(cbrt(x * x * x), IsAlmostEqualTo(x));
+ EXPECT_THAT(cbrt(y) * cbrt(y) * cbrt(y), IsAlmostEqualTo(y));
+ EXPECT_THAT(cbrt(x), IsAlmostEqualTo(pow(x, 1.0 / 3.0)));
- { // Check that cbrt(y) * cbrt(y) * cbrt(y) == y.
- J z = cbrt(y);
- J w = z * z * z;
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(w, y);
- }
-
- { // Check that cbrt(x) == pow(x, 1/3).
- J z = cbrt(x);
- J w = pow(x, 1.0 / 3.0);
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(z, w);
- }
NumericalTest("cbrt", cbrt<double, 2>, -1.0);
NumericalTest("cbrt", cbrt<double, 2>, -1e-5);
NumericalTest("cbrt", cbrt<double, 2>, 1e-5);
NumericalTest("cbrt", cbrt<double, 2>, 1.0);
+}
- { // Check that log1p(x) == log(1 + x)
- J z = log1p(x);
- J w = log(J{1} + x);
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(z, w);
- }
+TEST(Jet, Log1p) {
+ EXPECT_THAT(log1p(expm1(x)), IsAlmostEqualTo(x));
+ EXPECT_THAT(log1p(x), IsAlmostEqualTo(log(J{1} + x)));
- { // Check that log1p(x) does not loose precision for small x
+ { // log1p(x) does not loose precision for small x
J x = MakeJet(1e-16, 1e-8, 1e-4);
- J z = log1p(x);
- J w = MakeJet(9.9999999999999998e-17, 1e-8, 1e-4);
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(z, w);
+ EXPECT_THAT(log1p(x),
+ IsAlmostEqualTo(MakeJet(9.9999999999999998e-17, 1e-8, 1e-4)));
// log(1 + x) collapes to 0
J v = log(J{1} + x);
EXPECT_TRUE(v.a == 0);
}
+}
- { // Check that expm1(x) == exp(x) - 1
- J z = expm1(x);
- J w = exp(x) - J{1};
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(z, w);
- }
+TEST(Jet, Expm1) {
+ EXPECT_THAT(expm1(log1p(x)), IsAlmostEqualTo(x));
+ EXPECT_THAT(expm1(x), IsAlmostEqualTo(exp(x) - 1.0));
- { // Check that expm1(x) does not loose precision for small x
+ { // expm1(x) does not loose precision for small x
J x = MakeJet(9.9999999999999998e-17, 1e-8, 1e-4);
- J z = expm1(x);
- J w = MakeJet(1e-16, 1e-8, 1e-4);
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(z, w);
+ EXPECT_THAT(expm1(x), IsAlmostEqualTo(MakeJet(1e-16, 1e-8, 1e-4)));
// exp(x) - 1 collapes to 0
J v = exp(x) - J{1};
EXPECT_TRUE(v.a == 0);
}
+}
- { // Check that exp2(x) == exp(x * log(2))
- J z = exp2(x);
- J w = exp(x * log(2.0));
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(z, w);
- }
+TEST(Jet, Exp2) {
+ EXPECT_THAT(exp2(x), IsAlmostEqualTo(exp(x * log(2.0))));
NumericalTest("exp2", exp2<double, 2>, -1.0);
NumericalTest("exp2", exp2<double, 2>, -1e-5);
NumericalTest("exp2", exp2<double, 2>, -1e-200);
@@ -703,97 +372,152 @@
NumericalTest("exp2", exp2<double, 2>, 1e-200);
NumericalTest("exp2", exp2<double, 2>, 1e-5);
NumericalTest("exp2", exp2<double, 2>, 1.0);
+}
- { // Check that log10(x) == log(x) / log(10)
- J z = log10(x);
- J w = log(x) / log(10.0);
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(z, w);
- }
+TEST(Jet, Log) { EXPECT_THAT(log(exp(x)), IsAlmostEqualTo(x)); }
+
+TEST(Jet, Log10) {
+ EXPECT_THAT(log10(x), IsAlmostEqualTo(log(x) / log(10)));
NumericalTest("log10", log10<double, 2>, 1e-5);
NumericalTest("log10", log10<double, 2>, 1.0);
NumericalTest("log10", log10<double, 2>, 98.76);
+}
- { // Check that log2(x) == log(x) / log(2)
- J z = log2(x);
- J w = log(x) / log(2.0);
- VL << "z = " << z;
- VL << "w = " << w;
- ExpectJetsClose(z, w);
- }
+TEST(Jet, Log2) {
+ EXPECT_THAT(log2(x), IsAlmostEqualTo(log(x) / log(2)));
NumericalTest("log2", log2<double, 2>, 1e-5);
NumericalTest("log2", log2<double, 2>, 1.0);
NumericalTest("log2", log2<double, 2>, 100.0);
+}
- { // Check that norm(x) == x^2
- J v = norm(x);
- J w = x * x;
- VL << "v = " << v;
- VL << "w = " << w;
- ExpectJetsClose(v, w);
+TEST(Jet, Norm) {
+ EXPECT_THAT(norm(x), IsAlmostEqualTo(x * x));
+ EXPECT_THAT(norm(-x), IsAlmostEqualTo(x * x));
+}
+
+TEST(Jet, Pow) {
+ EXPECT_THAT(pow(x, 1.0), IsAlmostEqualTo(x));
+ EXPECT_THAT(pow(x, MakeJet(1.0, 0.0, 0.0)), IsAlmostEqualTo(x));
+ EXPECT_THAT(pow(kE, log(x)), IsAlmostEqualTo(x));
+ EXPECT_THAT(pow(MakeJet(kE, 0., 0.), log(x)), IsAlmostEqualTo(x));
+ EXPECT_THAT(pow(x, y),
+ IsAlmostEqualTo(pow(MakeJet(kE, 0.0, 0.0), y * log(x))));
+
+ // Specially cases
+
+ // pow(0, y) == 0 for y > 1, with both arguments Jets.
+ EXPECT_THAT(pow(MakeJet(0, 1, 2), MakeJet(2, 3, 4)),
+ IsAlmostEqualTo(MakeJet(0, 0, 0)));
+
+ // pow(0, y) == 0 for y == 1, with both arguments Jets.
+ EXPECT_THAT(pow(MakeJet(0, 1, 2), MakeJet(1, 3, 4)),
+ IsAlmostEqualTo(MakeJet(0, 1, 2)));
+
+ // pow(0, <1) is not finite, with both arguments Jets.
+ {
+ for (int i = 1; i < 10; i++) {
+ J a = MakeJet(0, 1, 2);
+ J b = MakeJet(i * 0.1, 3, 4); // b = 0.1 ... 0.9
+ J c = pow(a, b);
+ EXPECT_EQ(c.a, 0.0) << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ EXPECT_FALSE(IsFinite(c.v[0]))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ EXPECT_FALSE(IsFinite(c.v[1]))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ }
+
+ for (int i = -10; i < 0; i++) {
+ J a = MakeJet(0, 1, 2);
+ J b = MakeJet(i * 0.1, 3, 4); // b = -1,-0.9 ... -0.1
+ J c = pow(a, b);
+ EXPECT_FALSE(IsFinite(c.a))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ EXPECT_FALSE(IsFinite(c.v[0]))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ EXPECT_FALSE(IsFinite(c.v[1]))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ }
+
+ // The special case of 0^0 = 1 defined by the C standard.
+ {
+ J a = MakeJet(0, 1, 2);
+ J b = MakeJet(0, 3, 4);
+ J c = pow(a, b);
+ EXPECT_EQ(c.a, 1.0) << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ EXPECT_FALSE(IsFinite(c.v[0]))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ EXPECT_FALSE(IsFinite(c.v[1]))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ }
}
- { // Check that norm(-x) == x^2
- J v = norm(-x);
- J w = x * x;
- VL << "v = " << v;
- VL << "w = " << w;
- ExpectJetsClose(v, w);
+ // pow(<0, b) is correct for integer b.
+ {
+ J a = MakeJet(-1.5, 3, 4);
+
+ // b integer:
+ for (int i = -10; i <= 10; i++) {
+ J b = MakeJet(i, 0, 5);
+ J c = pow(a, b);
+
+ EXPECT_TRUE(AreAlmostEqual(c.a, pow(-1.5, i), kTolerance))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ EXPECT_TRUE(IsFinite(c.v[0]))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ EXPECT_FALSE(IsFinite(c.v[1]))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ EXPECT_TRUE(
+ AreAlmostEqual(c.v[0], i * pow(-1.5, i - 1) * 3.0, kTolerance))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ }
}
- { // Check that hypot(x, y) == sqrt(x^2 + y^2)
- J h = hypot(x, y);
- J s = sqrt(x * x + y * y);
- VL << "h = " << h;
- VL << "s = " << s;
- ExpectJetsClose(h, s);
+ // pow(<0, b) is correct for noninteger b.
+ {
+ J a = MakeJet(-1.5, 3, 4);
+ J b = MakeJet(-2.5, 0, 5);
+ J c = pow(a, b);
+ EXPECT_FALSE(IsFinite(c.a))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ EXPECT_FALSE(IsFinite(c.v[0]))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ EXPECT_FALSE(IsFinite(c.v[1]))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
}
- { // Check that hypot(x, x) == sqrt(2) * abs(x)
- J h = hypot(x, x);
- J s = sqrt(2.0) * abs(x);
- VL << "h = " << h;
- VL << "s = " << s;
- ExpectJetsClose(h, s);
+ // pow(0,y) == 0 for y == 2, with the second argument a Jet.
+ EXPECT_THAT(pow(0.0, MakeJet(2, 3, 4)), IsAlmostEqualTo(MakeJet(0, 0, 0)));
+
+ // pow(<0,y) is correct for integer y.
+ {
+ double a = -1.5;
+ for (int i = -10; i <= 10; i++) {
+ J b = MakeJet(i, 3, 0);
+ J c = pow(a, b);
+ ExpectClose(c.a, pow(-1.5, i), kTolerance);
+ EXPECT_FALSE(IsFinite(c.v[0]))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ EXPECT_TRUE(IsFinite(c.v[1]))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ ExpectClose(c.v[1], 0, kTolerance);
+ }
}
- { // Check that the derivative is zero tangentially to the circle:
- J h = hypot(MakeJet(2.0, 1.0, 1.0), MakeJet(2.0, 1.0, -1.0));
- VL << "h = " << h;
- ExpectJetsClose(h, MakeJet(sqrt(8.0), std::sqrt(2.0), 0.0));
+ // pow(<0,y) is correct for noninteger y.
+ {
+ double a = -1.5;
+ J b = MakeJet(-3.14, 3, 0);
+ J c = pow(a, b);
+ EXPECT_FALSE(IsFinite(c.a))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ EXPECT_FALSE(IsFinite(c.v[0]))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
+ EXPECT_FALSE(IsFinite(c.v[1]))
+ << "\na: " << a << "\nb: " << b << "\na^b: " << c;
}
+}
- { // Check that hypot(x, 0) == x
- J zero = MakeJet(0.0, 2.0, 3.14);
- J h = hypot(x, zero);
- VL << "h = " << h;
- ExpectJetsClose(x, h);
- }
-
- { // Check that hypot(0, y) == y
- J zero = MakeJet(0.0, 2.0, 3.14);
- J h = hypot(zero, y);
- VL << "h = " << h;
- ExpectJetsClose(y, h);
- }
-
- { // Check that hypot(x, 0) == sqrt(x * x) == x, even when x * x underflows:
- EXPECT_EQ(DBL_MIN * DBL_MIN, 0.0); // Make sure it underflows
- J huge = MakeJet(DBL_MIN, 2.0, 3.14);
- J h = hypot(huge, J(0.0));
- VL << "h = " << h;
- ExpectJetsClose(h, huge);
- }
-
- { // Check that hypot(x, 0) == sqrt(x * x) == x, even when x * x overflows:
- EXPECT_EQ(DBL_MAX * DBL_MAX, std::numeric_limits<double>::infinity());
- J huge = MakeJet(DBL_MAX, 2.0, 3.14);
- J h = hypot(huge, J(0.0));
- VL << "h = " << h;
- ExpectJetsClose(h, huge);
- }
-
+TEST(Jet, Hypot2) {
// Resolve the ambiguity between two and three argument hypot overloads
using Hypot2 = J(const J&, const J&);
Hypot2* const hypot2 = static_cast<Hypot2*>(&hypot<double, 2>);
@@ -810,372 +534,238 @@
NumericalTest2("hypot2", hypot2, 1.0, 2.0);
// clang-format on
+ J zero = MakeJet(0.0, 2.0, 3.14);
+ EXPECT_THAT(hypot(x, y), IsAlmostEqualTo(sqrt(x * x + y * y)));
+ EXPECT_THAT(hypot(x, x), IsAlmostEqualTo(sqrt(2.0) * abs(x)));
+
+ // The derivative is zero tangentially to the circle:
+ EXPECT_THAT(hypot(MakeJet(2.0, 1.0, 1.0), MakeJet(2.0, 1.0, -1.0)),
+ IsAlmostEqualTo(MakeJet(sqrt(8.0), std::sqrt(2.0), 0.0)));
+
+ EXPECT_THAT(hypot(zero, x), IsAlmostEqualTo(x));
+ EXPECT_THAT(hypot(y, zero), IsAlmostEqualTo(y));
+
+ // hypot(x, 0, 0) == x, even when x * x underflows:
+ EXPECT_EQ(
+ std::numeric_limits<double>::min() * std::numeric_limits<double>::min(),
+ 0.0); // Make sure it underflows
+ J tiny = MakeJet(std::numeric_limits<double>::min(), 2.0, 3.14);
+ EXPECT_THAT(hypot(tiny, J{0}), IsAlmostEqualTo(tiny));
+
+ // hypot(x, 0, 0) == x, even when x * x overflows:
+ EXPECT_EQ(
+ std::numeric_limits<double>::max() * std::numeric_limits<double>::max(),
+ std::numeric_limits<double>::infinity());
+ J huge = MakeJet(std::numeric_limits<double>::max(), 2.0, 3.14);
+ EXPECT_THAT(hypot(huge, J{0}), IsAlmostEqualTo(huge));
+}
+
#ifdef CERES_HAS_CPP17
- { // Check that hypot(x, y) == sqrt(x^2 + y^2)
- J h = hypot(x, y, z);
- J s = sqrt(x * x + y * y + z * z);
- VL << "h = " << h;
- VL << "s = " << s;
- ExpectJetsClose(h, s);
- }
+TEST(Jet, Hypot3) {
+ J zero = MakeJet(0.0, 2.0, 3.14);
- { // Check that hypot(x, x) == sqrt(3) * abs(x)
- J h = hypot(x, x, x);
- J s = sqrt(3.0) * abs(x);
- VL << "h = " << h;
- VL << "s = " << s;
- ExpectJetsClose(h, s);
- }
+ // hypot(x, y, z) == sqrt(x^2 + y^2 + z^2)
+ EXPECT_THAT(hypot(x, y, z), IsAlmostEqualTo(sqrt(x * x + y * y + z * z)));
- { // Check that the derivative is zero tangentially to the circle:
- J h = hypot(MakeJet(2.0, 1.0, 1.0),
- MakeJet(2.0, 1.0, -1.0),
- MakeJet(2.0, -1.0, 0.0));
- VL << "h = " << h;
- ExpectJetsClose(h, MakeJet(sqrt(12.0), 1.0 / std::sqrt(3.0), 0.0));
- }
+ // hypot(x, x) == sqrt(3) * abs(x)
+ EXPECT_THAT(hypot(x, x, x), IsAlmostEqualTo(sqrt(3.0) * abs(x)));
- { // Check that hypot(x, 0, 0) == x
- J zero = MakeJet(0.0, 2.0, 3.14);
- J h = hypot(x, zero, zero);
- VL << "h = " << h;
- ExpectJetsClose(x, h);
- }
+ // The derivative is zero tangentially to the circle:
+ EXPECT_THAT(hypot(MakeJet(2.0, 1.0, 1.0),
+ MakeJet(2.0, 1.0, -1.0),
+ MakeJet(2.0, -1.0, 0.0)),
+ IsAlmostEqualTo(MakeJet(sqrt(12.0), 1.0 / std::sqrt(3.0), 0.0)));
- { // Check that hypot(0, y, 0) == y
- J zero = MakeJet(0.0, 2.0, 3.14);
- J h = hypot(zero, y, zero);
- VL << "h = " << h;
- ExpectJetsClose(y, h);
- }
+ EXPECT_THAT(hypot(x, zero, zero), IsAlmostEqualTo(x));
+ EXPECT_THAT(hypot(zero, y, zero), IsAlmostEqualTo(y));
+ EXPECT_THAT(hypot(zero, zero, z), IsAlmostEqualTo(z));
+ EXPECT_THAT(hypot(x, y, z), IsAlmostEqualTo(hypot(hypot(x, y), z)));
+ EXPECT_THAT(hypot(x, y, z), IsAlmostEqualTo(hypot(x, hypot(y, z))));
- { // Check that hypot(0, 0, z) == z
- J zero = MakeJet(0.0, 2.0, 3.14);
- J h = hypot(zero, zero, z);
- VL << "h = " << h;
- ExpectJetsClose(z, h);
- }
+ // The following two tests are disabled because the three argument hypot is
+ // broken in the libc++ shipped with CLANG as of January 2022.
- { // Check that hypot(x, y, z) == hypot(hypot(x, y), z)
- J v = hypot(x, y, z);
- J w = hypot(hypot(x, y), z);
- VL << "v = " << v;
- VL << "w = " << w;
- ExpectJetsClose(v, w);
- }
+#if !defined(_LIBCPP_VERSION)
+ // hypot(x, 0, 0) == x, even when x * x underflows:
+ EXPECT_EQ(
+ std::numeric_limits<double>::min() * std::numeric_limits<double>::min(),
+ 0.0); // Make sure it underflows
+ J tiny = MakeJet(std::numeric_limits<double>::min(), 2.0, 3.14);
+ EXPECT_THAT(hypot(tiny, J{0}, J{0}), IsAlmostEqualTo(tiny));
- { // Check that hypot(x, y, z) == hypot(x, hypot(y, z))
- J v = hypot(x, y, z);
- J w = hypot(x, hypot(y, z));
- VL << "v = " << v;
- VL << "w = " << w;
- ExpectJetsClose(v, w);
- }
+ // hypot(x, 0, 0) == x, even when x * x overflows:
+ EXPECT_EQ(
+ std::numeric_limits<double>::max() * std::numeric_limits<double>::max(),
+ std::numeric_limits<double>::infinity());
+ J huge = MakeJet(std::numeric_limits<double>::max(), 2.0, 3.14);
+ EXPECT_THAT(hypot(huge, J{0}, J{0}), IsAlmostEqualTo(huge));
+#endif
+}
- { // Check that hypot(x, 0, 0) == sqrt(x * x) == x, even when x * x
- // underflows:
- EXPECT_EQ(
- std::numeric_limits<double>::min() * std::numeric_limits<double>::min(),
- 0.0); // Make sure it underflows
- J huge = MakeJet(std::numeric_limits<double>::min(), 2.0, 3.14);
- J h = hypot(huge, J(0.0), J(0.0));
- VL << "h = " << h;
- ExpectJetsClose(h, huge);
- }
-
- { // Check that hypot(x, 0, 0) == sqrt(x * x) == x, even when x * x
- // overflows:
- EXPECT_EQ(
- std::numeric_limits<double>::max() * std::numeric_limits<double>::max(),
- std::numeric_limits<double>::infinity());
- J huge = MakeJet(std::numeric_limits<double>::max(), 2.0, 3.14);
- J h = hypot(huge, J(0.0), J(0.0));
- VL << "h = " << h;
- ExpectJetsClose(h, huge);
- }
#endif // defined(CERES_HAS_CPP17)
#ifdef CERES_HAS_CPP20
- { // Check lerp(x, y, 0) == x
- J z = lerp(x, y, J{0});
- VL << "z = " << z;
- ExpectJetsClose(z, x);
- }
- { // Check lerp(x, y, 1) == y
- J z = lerp(x, y, J{1});
- VL << "z = " << z;
- ExpectJetsClose(z, y);
- }
+TEST(Jet, Lerp) {
+ EXPECT_THAT(lerp(x, y, J{0}), IsAlmostEqualTo(x));
+ EXPECT_THAT(lerp(x, y, J{1}), IsAlmostEqualTo(y));
+ EXPECT_THAT(lerp(x, x, J{1}), IsAlmostEqualTo(x));
+ EXPECT_THAT(lerp(y, y, J{0}), IsAlmostEqualTo(y));
+ EXPECT_THAT(lerp(x, y, J{0.5}), IsAlmostEqualTo((x + y) / J{2.0}));
+ EXPECT_THAT(lerp(x, y, J{2}), IsAlmostEqualTo(J{2.0} * y - x));
+ EXPECT_THAT(lerp(x, y, J{-2}), IsAlmostEqualTo(J{3.0} * x - J{2} * x));
+}
- { // Check lerp(x, x, 1) == x
- J z = lerp(x, x, J{1});
- VL << "z = " << z;
- ExpectJetsClose(z, x);
- }
+TEST(Jet, Midpoint) {
+ EXPECT_THAT(midpoint(x, y), IsAlmostEqualTo((x + y) / J{2}));
+ EXPECT_THAT(midpoint(x, x), IsAlmostEqualTo(x));
- { // Check lerp(y, y, 0) == y
- J z = lerp(y, y, J{1});
- VL << "z = " << z;
- ExpectJetsClose(z, y);
- }
-
- { // Check lerp(x, y, 0.5) == (x + y) / 2
- J z = lerp(x, y, J{0.5});
- J v = (x + y) / J{2};
- VL << "z = " << z;
- VL << "v = " << v;
- ExpectJetsClose(z, v);
- }
-
- { // Check lerp(x, y, 2) == 2y - x
- J z = lerp(x, y, J{2});
- J v = J{2} * y - x;
- VL << "z = " << z;
- VL << "v = " << v;
- ExpectJetsClose(z, v);
- }
-
- { // Check lerp(x, y, -2) == 3x - 2y
- J z = lerp(x, y, -J{2});
- J v = J{3} * x - J{2} * y;
- VL << "z = " << z;
- VL << "v = " << v;
- ExpectJetsClose(z, v);
- }
-
- { // Check that midpoint(x, y) = (x + y) / 2
- J z = midpoint(x, y);
- J v = (x + y) / J{2};
- VL << "z = " << z;
- VL << "v = " << v;
- ExpectJetsClose(z, v);
- }
-
- { // Check that midpoint(x, x) = x
- J z = midpoint(x, x);
- VL << "z = " << z;
- ExpectJetsClose(z, x);
- }
-
- { // Check that midpoint(x, y) = (x + y) / 2 while avoiding overflow
+ {
+ // midpoint(x, y) = (x + y) / 2 while avoiding overflow
J x = MakeJet(std::numeric_limits<double>::min(), 1, 2);
J y = MakeJet(std::numeric_limits<double>::max(), 3, 4);
- J z = midpoint(x, y);
- J v = x + (y - x) / J{2};
- VL << "z = " << z;
- VL << "v = " << v;
- ExpectJetsClose(z, v);
+ EXPECT_THAT(midpoint(x, y), IsAlmostEqualTo(x + (y - x) / J{2}));
}
- { // Check that midpoint(x, x) = x while avoiding overflow
- constexpr double a = std::numeric_limits<double>::max();
- J x = MakeJet(a, a, a);
- J z = midpoint(x, x);
- VL << "z = " << z;
- ExpectJetsClose(z, x);
+ {
+ // midpoint(x, x) = x while avoiding overflow
+ J x = MakeJet(std::numeric_limits<double>::max(),
+ std::numeric_limits<double>::max(),
+ std::numeric_limits<double>::max());
+ EXPECT_THAT(midpoint(x, x), IsAlmostEqualTo(x));
}
- { // Check that midpoint does not overflow for very large values
+ { // midpoint does not overflow for very large values
constexpr double a = 0.75 * std::numeric_limits<double>::max();
J x = MakeJet(a, a, -a);
J y = MakeJet(a, a, a);
- J z = midpoint(x, y);
- VL << "z = " << z;
- ExpectJetsClose(z, MakeJet(a, a, 0));
+ EXPECT_THAT(midpoint(x, y), IsAlmostEqualTo(MakeJet(a, a, 0)));
}
+}
+
#endif // defined(CERES_HAS_CPP20)
- {
- J z = fmax(x, y);
- VL << "z = " << z;
- ExpectJetsClose(x, z);
- }
- {
- J z = fmax(y, x);
- VL << "z = " << z;
- ExpectJetsClose(x, z);
- }
- {
- J z = fmax(x, y.a);
- VL << "z = " << z;
- ExpectJetsClose(x, z);
- }
- {
- J z = fmax(y, x.a);
- VL << "z = " << z;
- ExpectJetsClose(J{x.a}, z);
- }
- {
- J z = fmax(x.a, y);
- VL << "z = " << z;
- ExpectJetsClose(J{x.a}, z);
- }
- {
- J z = fmax(y.a, x);
- VL << "z = " << z;
- ExpectJetsClose(x, z);
- }
- {
- J z = fmax(std::numeric_limits<double>::quiet_NaN(), x);
- VL << "z = " << z;
- ExpectJetsClose(x, z);
- }
- {
- J z = fmax(x, std::numeric_limits<double>::quiet_NaN());
- VL << "z = " << z;
- ExpectJetsClose(x, z);
- }
+TEST(Jet, Fmax) {
+ EXPECT_THAT(fmax(x, y), IsAlmostEqualTo(x));
+ EXPECT_THAT(fmax(y, x), IsAlmostEqualTo(x));
+ EXPECT_THAT(fmax(x, y.a), IsAlmostEqualTo(x));
+ EXPECT_THAT(fmax(y.a, x), IsAlmostEqualTo(x));
+ EXPECT_THAT(fmax(y, x.a), IsAlmostEqualTo(J{x.a}));
+ EXPECT_THAT(fmax(x.a, y), IsAlmostEqualTo(J{x.a}));
+ EXPECT_THAT(fmax(x, std::numeric_limits<double>::quiet_NaN()),
+ IsAlmostEqualTo(x));
+ EXPECT_THAT(fmax(std::numeric_limits<double>::quiet_NaN(), x),
+ IsAlmostEqualTo(x));
+}
- {
- J z = fmin(x, y);
- VL << "z = " << z;
- ExpectJetsClose(y, z);
- }
- {
- J z = fmin(y, x);
- VL << "z = " << z;
- ExpectJetsClose(y, z);
- }
- {
- J z = fmin(x, y.a);
- VL << "z = " << z;
- ExpectJetsClose(J{y.a}, z);
- }
- {
- J z = fmin(y, x.a);
- VL << "z = " << z;
- ExpectJetsClose(y, z);
- }
- {
- J z = fmin(x.a, y);
- VL << "z = " << z;
- ExpectJetsClose(y, z);
- }
- {
- J z = fmin(y.a, x);
- VL << "z = " << z;
- ExpectJetsClose(J{y.a}, z);
- }
- {
- J z = fmin(x, std::numeric_limits<double>::quiet_NaN());
- VL << "z = " << z;
- ExpectJetsClose(x, z);
- }
- {
- J z = fmin(std::numeric_limits<double>::quiet_NaN(), x);
- VL << "z = " << z;
- ExpectJetsClose(x, z);
- }
+TEST(Jet, Fmin) {
+ EXPECT_THAT(fmin(x, y), IsAlmostEqualTo(y));
+ EXPECT_THAT(fmin(y, x), IsAlmostEqualTo(y));
+ EXPECT_THAT(fmin(x, y.a), IsAlmostEqualTo(J{y.a}));
+ EXPECT_THAT(fmin(y.a, x), IsAlmostEqualTo(J{y.a}));
+ EXPECT_THAT(fmin(y, x.a), IsAlmostEqualTo(y));
+ EXPECT_THAT(fmin(x.a, y), IsAlmostEqualTo(y));
+ EXPECT_THAT(fmin(x, std::numeric_limits<double>::quiet_NaN()),
+ IsAlmostEqualTo(x));
+ EXPECT_THAT(fmin(std::numeric_limits<double>::quiet_NaN(), x),
+ IsAlmostEqualTo(x));
+}
+TEST(Jet, CopySign) {
{ // copysign(x, +1)
J z = copysign(x, J{+1});
- VL << "z = " << z;
- ExpectJetsClose(x, z);
- EXPECT_TRUE(IsFinite(z.v[0]));
- EXPECT_TRUE(IsFinite(z.v[1]));
+ EXPECT_THAT(z, IsAlmostEqualTo(x));
+ EXPECT_TRUE(IsFinite(z.v[0])) << z;
+ EXPECT_TRUE(IsFinite(z.v[1])) << z;
}
{ // copysign(x, -1)
J z = copysign(x, J{-1});
- VL << "z = " << z;
- ExpectJetsClose(-x, z);
- EXPECT_TRUE(IsFinite(z.v[0]));
- EXPECT_TRUE(IsFinite(z.v[1]));
+ EXPECT_THAT(z, IsAlmostEqualTo(-x));
+ EXPECT_TRUE(IsFinite(z.v[0])) << z;
+ EXPECT_TRUE(IsFinite(z.v[1])) << z;
}
{ // copysign(-x, +1)
J z = copysign(-x, J{+1});
- VL << "z = " << z;
- ExpectJetsClose(x, z);
- EXPECT_TRUE(IsFinite(z.v[0]));
- EXPECT_TRUE(IsFinite(z.v[1]));
+ EXPECT_THAT(z, IsAlmostEqualTo(x));
+ EXPECT_TRUE(IsFinite(z.v[0])) << z;
+ EXPECT_TRUE(IsFinite(z.v[1])) << z;
}
{ // copysign(-x, -1)
J z = copysign(-x, J{-1});
- VL << "z = " << z;
- ExpectJetsClose(-x, z);
- EXPECT_TRUE(IsFinite(z.v[0]));
- EXPECT_TRUE(IsFinite(z.v[1]));
+ EXPECT_THAT(z, IsAlmostEqualTo(-x));
+ EXPECT_TRUE(IsFinite(z.v[0])) << z;
+ EXPECT_TRUE(IsFinite(z.v[1])) << z;
}
{ // copysign(-0, +1)
J z = copysign(MakeJet(-0, 1, 2), J{+1});
- VL << "z = " << z;
- ExpectJetsClose(MakeJet(+0, 1, 2), z);
- EXPECT_FALSE(std::signbit(z.a));
- EXPECT_TRUE(IsFinite(z.v[0]));
- EXPECT_TRUE(IsFinite(z.v[1]));
+ EXPECT_THAT(z, IsAlmostEqualTo(MakeJet(+0, 1, 2)));
+ EXPECT_FALSE(std::signbit(z.a)) << z;
+ EXPECT_TRUE(IsFinite(z.v[0])) << z;
+ EXPECT_TRUE(IsFinite(z.v[1])) << z;
}
{ // copysign(-0, -1)
J z = copysign(MakeJet(-0, 1, 2), J{-1});
- VL << "z = " << z;
- ExpectJetsClose(MakeJet(-0, -1, -2), z);
- EXPECT_TRUE(std::signbit(z.a));
- EXPECT_TRUE(IsFinite(z.v[0]));
- EXPECT_TRUE(IsFinite(z.v[1]));
+ EXPECT_THAT(z, IsAlmostEqualTo(MakeJet(-0, -1, -2)));
+ EXPECT_TRUE(std::signbit(z.a)) << z;
+ EXPECT_TRUE(IsFinite(z.v[0])) << z;
+ EXPECT_TRUE(IsFinite(z.v[1])) << z;
}
{ // copysign(+0, -1)
J z = copysign(MakeJet(+0, 1, 2), J{-1});
- VL << "z = " << z;
- ExpectJetsClose(MakeJet(-0, -1, -2), z);
- EXPECT_TRUE(std::signbit(z.a));
- EXPECT_TRUE(IsFinite(z.v[0]));
- EXPECT_TRUE(IsFinite(z.v[1]));
+ EXPECT_THAT(z, IsAlmostEqualTo(MakeJet(-0, -1, -2)));
+ EXPECT_TRUE(std::signbit(z.a)) << z;
+ EXPECT_TRUE(IsFinite(z.v[0])) << z;
+ EXPECT_TRUE(IsFinite(z.v[1])) << z;
}
{ // copysign(+0, +1)
J z = copysign(MakeJet(+0, 1, 2), J{+1});
- VL << "z = " << z;
- ExpectJetsClose(MakeJet(+0, 1, 2), z);
- EXPECT_FALSE(std::signbit(z.a));
- EXPECT_TRUE(IsFinite(z.v[0]));
- EXPECT_TRUE(IsFinite(z.v[1]));
+ EXPECT_THAT(z, IsAlmostEqualTo(MakeJet(+0, 1, 2)));
+ EXPECT_FALSE(std::signbit(z.a)) << z;
+ EXPECT_TRUE(IsFinite(z.v[0])) << z;
+ EXPECT_TRUE(IsFinite(z.v[1])) << z;
}
{ // copysign(+0, +0)
J z = copysign(MakeJet(+0, 1, 2), J{+0});
- VL << "z = " << z;
- EXPECT_FALSE(std::signbit(z.a));
- EXPECT_TRUE(IsNaN(z.v[0]));
- EXPECT_TRUE(IsNaN(z.v[1]));
+ EXPECT_FALSE(std::signbit(z.a)) << z;
+ EXPECT_TRUE(IsNaN(z.v[0])) << z;
+ EXPECT_TRUE(IsNaN(z.v[1])) << z;
}
{ // copysign(+0, -0)
J z = copysign(MakeJet(+0, 1, 2), J{-0});
- VL << "z = " << z;
- EXPECT_FALSE(std::signbit(z.a));
- EXPECT_TRUE(IsNaN(z.v[0]));
- EXPECT_TRUE(IsNaN(z.v[1]));
+ EXPECT_FALSE(std::signbit(z.a)) << z;
+ EXPECT_TRUE(IsNaN(z.v[0])) << z;
+ EXPECT_TRUE(IsNaN(z.v[1])) << z;
}
{ // copysign(-0, +0)
J z = copysign(MakeJet(-0, 1, 2), J{+0});
- VL << "z = " << z;
- EXPECT_FALSE(std::signbit(z.a));
- EXPECT_TRUE(IsNaN(z.v[0]));
- EXPECT_TRUE(IsNaN(z.v[1]));
+ EXPECT_FALSE(std::signbit(z.a)) << z;
+ EXPECT_TRUE(IsNaN(z.v[0])) << z;
+ EXPECT_TRUE(IsNaN(z.v[1])) << z;
}
{ // copysign(-0, -0)
J z = copysign(MakeJet(-0, 1, 2), J{-0});
- VL << "z = " << z;
- EXPECT_FALSE(std::signbit(z.a));
- EXPECT_TRUE(IsNaN(z.v[0]));
- EXPECT_TRUE(IsNaN(z.v[1]));
+ EXPECT_FALSE(std::signbit(z.a)) << z;
+ EXPECT_TRUE(IsNaN(z.v[0])) << z;
+ EXPECT_TRUE(IsNaN(z.v[1])) << z;
}
{ // copysign(1, -nan)
J z = copysign(MakeJet(1, 2, 3),
-J{std::numeric_limits<double>::quiet_NaN()});
- VL << "z = " << z;
- EXPECT_TRUE(std::signbit(z.a));
- EXPECT_TRUE(std::signbit(z.v[0]));
- EXPECT_TRUE(std::signbit(z.v[1]));
- EXPECT_FALSE(IsNaN(z.v[0]));
- EXPECT_FALSE(IsNaN(z.v[1]));
+ EXPECT_TRUE(std::signbit(z.a)) << z;
+ EXPECT_TRUE(std::signbit(z.v[0])) << z;
+ EXPECT_TRUE(std::signbit(z.v[1])) << z;
+ EXPECT_FALSE(IsNaN(z.v[0])) << z;
+ EXPECT_FALSE(IsNaN(z.v[1])) << z;
}
{ // copysign(1, +nan)
J z = copysign(MakeJet(1, 2, 3),
+J{std::numeric_limits<double>::quiet_NaN()});
- VL << "z = " << z;
- EXPECT_FALSE(std::signbit(z.a));
- EXPECT_FALSE(std::signbit(z.v[0]));
- EXPECT_FALSE(std::signbit(z.v[1]));
- EXPECT_FALSE(IsNaN(z.v[0]));
- EXPECT_FALSE(IsNaN(z.v[1]));
+ EXPECT_FALSE(std::signbit(z.a)) << z;
+ EXPECT_FALSE(std::signbit(z.v[0])) << z;
+ EXPECT_FALSE(std::signbit(z.v[1])) << z;
+ EXPECT_FALSE(IsNaN(z.v[0])) << z;
+ EXPECT_FALSE(IsNaN(z.v[1])) << z;
}
}
@@ -1191,12 +781,12 @@
M << x, y, z, w;
v << x, z;
- // Check that M * v == (v^T * M^T)^T
+ // M * v == (v^T * M^T)^T
r1 = M * v;
r2 = (v.transpose() * M.transpose()).transpose();
- ExpectJetsClose(r1(0), r2(0));
- ExpectJetsClose(r1(1), r2(1));
+ EXPECT_THAT(r1(0), IsAlmostEqualTo(r2(0)));
+ EXPECT_THAT(r1(1), IsAlmostEqualTo(r2(1)));
}
TEST(JetTraitsTest, ClassificationMixed) {
@@ -1307,7 +897,7 @@
const J sum = a.sum();
const J sum2 = a(0) + a(1);
- ExpectJetsClose(sum, sum2);
+ EXPECT_THAT(sum, IsAlmostEqualTo(sum2));
}
TEST(JetTraitsTest, MatrixScalarBinaryOps) {
@@ -1322,22 +912,22 @@
M << x, y, z, w;
v << 0.6, -2.1;
- // Check that M * v == M * v.cast<J>().
+ // M * v == M * v.cast<J>().
const Eigen::Matrix<J, 2, 1> r1 = M * v;
const Eigen::Matrix<J, 2, 1> r2 = M * v.cast<J>();
- ExpectJetsClose(r1(0), r2(0));
- ExpectJetsClose(r1(1), r2(1));
+ EXPECT_THAT(r1(0), IsAlmostEqualTo(r2(0)));
+ EXPECT_THAT(r1(1), IsAlmostEqualTo(r2(1)));
- // Check that M * a == M * T(a).
+ // M * a == M * T(a).
const double a = 3.1;
const Eigen::Matrix<J, 2, 2> r3 = M * a;
const Eigen::Matrix<J, 2, 2> r4 = M * J(a);
- ExpectJetsClose(r3(0, 0), r4(0, 0));
- ExpectJetsClose(r3(1, 0), r4(1, 0));
- ExpectJetsClose(r3(0, 1), r4(0, 1));
- ExpectJetsClose(r3(1, 1), r4(1, 1));
+ EXPECT_THAT(r3(0, 0), IsAlmostEqualTo(r4(0, 0)));
+ EXPECT_THAT(r3(0, 1), IsAlmostEqualTo(r4(0, 1)));
+ EXPECT_THAT(r3(1, 0), IsAlmostEqualTo(r4(1, 0)));
+ EXPECT_THAT(r3(1, 1), IsAlmostEqualTo(r4(1, 1)));
}
TEST(JetTraitsTest, ArrayScalarUnaryOps) {
@@ -1348,7 +938,7 @@
const J sum = a.sum();
const J sum2 = a(0) + a(1);
- ExpectJetsClose(sum, sum2);
+ EXPECT_THAT(sum, sum2);
}
TEST(JetTraitsTest, ArrayScalarBinaryOps) {
@@ -1361,23 +951,23 @@
a << x, y;
b << 0.6, -2.1;
- // Check that a * b == a * b.cast<T>()
+ // a * b == a * b.cast<T>()
const Eigen::Array<J, 2, 1> r1 = a * b;
const Eigen::Array<J, 2, 1> r2 = a * b.cast<J>();
- ExpectJetsClose(r1(0), r2(0));
- ExpectJetsClose(r1(1), r2(1));
+ EXPECT_THAT(r1(0), r2(0));
+ EXPECT_THAT(r1(1), r2(1));
- // Check that a * c == a * T(c).
+ // a * c == a * T(c).
const double c = 3.1;
const Eigen::Array<J, 2, 1> r3 = a * c;
const Eigen::Array<J, 2, 1> r4 = a * J(c);
- ExpectJetsClose(r3(0), r3(0));
- ExpectJetsClose(r4(1), r4(1));
+ EXPECT_THAT(r3(0), r3(0));
+ EXPECT_THAT(r4(1), r4(1));
}
-TEST(Jet, nested3x) {
+TEST(Jet, Nested3X) {
typedef Jet<J, 2> JJ;
typedef Jet<JJ, 2> JJJ;
@@ -1422,7 +1012,7 @@
using J0 = Jet<T, 0>;
using J0d = J0<double>;
-TYPED_TEST(JetTest, comparison_jet) {
+TYPED_TEST(JetTest, Comparison) {
using Scalar = TypeParam;
EXPECT_EQ(J0<Scalar>{0}, J0<Scalar>{0});
@@ -1433,7 +1023,7 @@
EXPECT_NE(J0<Scalar>{1}, J0<Scalar>{2});
}
-TYPED_TEST(JetTest, comparison_scalar) {
+TYPED_TEST(JetTest, ScalarComparison) {
using Scalar = TypeParam;
EXPECT_EQ(J0d{0.0}, Scalar{0});
@@ -1451,7 +1041,7 @@
EXPECT_NE(Scalar{2}, J0d{1.0});
}
-TYPED_TEST(JetTest, comparison_nested2x) {
+TYPED_TEST(JetTest, Nested2XComparison) {
using Scalar = TypeParam;
EXPECT_EQ(J0<J0d>{J0d{0.0}}, Scalar{0});
@@ -1469,7 +1059,7 @@
EXPECT_NE(Scalar{2}, J0<J0d>{J0d{1.0}});
}
-TYPED_TEST(JetTest, comparison_nested3x) {
+TYPED_TEST(JetTest, Nested3XComparison) {
using Scalar = TypeParam;
EXPECT_EQ(J0<J0<J0d>>{J0<J0d>{J0d{0.0}}}, Scalar{0});
