345 lines
14 KiB
C++
345 lines
14 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include <sstream>
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#include "main.h"
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#define VERIFY_HALF_BITS_EQUAL(h, bits) \
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VERIFY_IS_EQUAL((numext::bit_cast<numext::uint16_t>(h)), (static_cast<numext::uint16_t>(bits)))
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// Make sure it's possible to forward declare Eigen::half
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namespace Eigen {
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struct half;
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}
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using Eigen::half;
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void test_conversion() {
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using Eigen::half_impl::__half_raw;
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// Round-trip bit-cast with uint16.
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VERIFY_IS_EQUAL(numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(1.0f))), half(1.0f));
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VERIFY_IS_EQUAL(numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(0.5f))), half(0.5f));
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VERIFY_IS_EQUAL(numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(-0.33333f))), half(-0.33333f));
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VERIFY_IS_EQUAL(numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(0.0f))), half(0.0f));
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// Conversion from float.
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VERIFY_HALF_BITS_EQUAL(half(1.0f), 0x3c00);
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VERIFY_HALF_BITS_EQUAL(half(0.5f), 0x3800);
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VERIFY_HALF_BITS_EQUAL(half(0.33333f), 0x3555);
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VERIFY_HALF_BITS_EQUAL(half(0.0f), 0x0000);
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VERIFY_HALF_BITS_EQUAL(half(-0.0f), 0x8000);
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VERIFY_HALF_BITS_EQUAL(half(65504.0f), 0x7bff);
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VERIFY_HALF_BITS_EQUAL(half(65536.0f), 0x7c00); // Becomes infinity.
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// Denormals.
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VERIFY_HALF_BITS_EQUAL(half(-5.96046e-08f), 0x8001);
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VERIFY_HALF_BITS_EQUAL(half(5.96046e-08f), 0x0001);
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VERIFY_HALF_BITS_EQUAL(half(1.19209e-07f), 0x0002);
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// Verify round-to-nearest-even behavior.
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float val1 = float(half(__half_raw(0x3c00)));
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float val2 = float(half(__half_raw(0x3c01)));
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float val3 = float(half(__half_raw(0x3c02)));
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VERIFY_HALF_BITS_EQUAL(half(0.5f * (val1 + val2)), 0x3c00);
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VERIFY_HALF_BITS_EQUAL(half(0.5f * (val2 + val3)), 0x3c02);
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// Conversion from int.
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VERIFY_HALF_BITS_EQUAL(half(-1), 0xbc00);
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VERIFY_HALF_BITS_EQUAL(half(0), 0x0000);
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VERIFY_HALF_BITS_EQUAL(half(1), 0x3c00);
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VERIFY_HALF_BITS_EQUAL(half(2), 0x4000);
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VERIFY_HALF_BITS_EQUAL(half(3), 0x4200);
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// Conversion from bool.
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VERIFY_HALF_BITS_EQUAL(half(false), 0x0000);
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VERIFY_HALF_BITS_EQUAL(half(true), 0x3c00);
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// Conversion to float.
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VERIFY_IS_EQUAL(float(half(__half_raw(0x0000))), 0.0f);
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VERIFY_IS_EQUAL(float(half(__half_raw(0x3c00))), 1.0f);
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// Denormals.
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VERIFY_IS_APPROX(float(half(__half_raw(0x8001))), -5.96046e-08f);
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VERIFY_IS_APPROX(float(half(__half_raw(0x0001))), 5.96046e-08f);
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VERIFY_IS_APPROX(float(half(__half_raw(0x0002))), 1.19209e-07f);
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// NaNs and infinities.
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VERIFY(!(numext::isinf)(float(half(65504.0f)))); // Largest finite number.
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VERIFY(!(numext::isnan)(float(half(0.0f))));
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VERIFY((numext::isinf)(float(half(__half_raw(0xfc00)))));
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VERIFY((numext::isnan)(float(half(__half_raw(0xfc01)))));
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VERIFY((numext::isinf)(float(half(__half_raw(0x7c00)))));
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VERIFY((numext::isnan)(float(half(__half_raw(0x7c01)))));
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#if !EIGEN_COMP_MSVC
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// Visual Studio errors out on divisions by 0
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VERIFY((numext::isnan)(float(half(0.0 / 0.0))));
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VERIFY((numext::isinf)(float(half(1.0 / 0.0))));
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VERIFY((numext::isinf)(float(half(-1.0 / 0.0))));
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#endif
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// Exactly same checks as above, just directly on the half representation.
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VERIFY(!(numext::isinf)(half(__half_raw(0x7bff))));
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VERIFY(!(numext::isnan)(half(__half_raw(0x0000))));
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VERIFY((numext::isinf)(half(__half_raw(0xfc00))));
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VERIFY((numext::isnan)(half(__half_raw(0xfc01))));
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VERIFY((numext::isinf)(half(__half_raw(0x7c00))));
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VERIFY((numext::isnan)(half(__half_raw(0x7c01))));
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#if !EIGEN_COMP_MSVC
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// Visual Studio errors out on divisions by 0
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VERIFY((numext::isnan)(half(0.0 / 0.0)));
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VERIFY((numext::isinf)(half(1.0 / 0.0)));
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VERIFY((numext::isinf)(half(-1.0 / 0.0)));
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#endif
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// Conversion to bool
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VERIFY(!static_cast<bool>(half(0.0)));
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VERIFY(!static_cast<bool>(half(-0.0)));
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VERIFY(static_cast<bool>(half(__half_raw(0x7bff))));
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VERIFY(static_cast<bool>(half(-0.33333)));
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VERIFY(static_cast<bool>(half(1.0)));
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VERIFY(static_cast<bool>(half(-1.0)));
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VERIFY(static_cast<bool>(half(-5.96046e-08f)));
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}
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void test_numtraits() {
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std::cout << "epsilon = " << NumTraits<half>::epsilon() << " (0x" << std::hex
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<< numext::bit_cast<numext::uint16_t>(NumTraits<half>::epsilon()) << ")" << std::endl;
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std::cout << "highest = " << NumTraits<half>::highest() << " (0x" << std::hex
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<< numext::bit_cast<numext::uint16_t>(NumTraits<half>::highest()) << ")" << std::endl;
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std::cout << "lowest = " << NumTraits<half>::lowest() << " (0x" << std::hex
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<< numext::bit_cast<numext::uint16_t>(NumTraits<half>::lowest()) << ")" << std::endl;
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std::cout << "min = " << (std::numeric_limits<half>::min)() << " (0x" << std::hex
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<< numext::bit_cast<numext::uint16_t>(half((std::numeric_limits<half>::min)())) << ")" << std::endl;
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std::cout << "denorm min = " << (std::numeric_limits<half>::denorm_min)() << " (0x" << std::hex
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<< numext::bit_cast<numext::uint16_t>(half((std::numeric_limits<half>::denorm_min)())) << ")" << std::endl;
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std::cout << "infinity = " << NumTraits<half>::infinity() << " (0x" << std::hex
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<< numext::bit_cast<numext::uint16_t>(NumTraits<half>::infinity()) << ")" << std::endl;
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std::cout << "quiet nan = " << NumTraits<half>::quiet_NaN() << " (0x" << std::hex
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<< numext::bit_cast<numext::uint16_t>(NumTraits<half>::quiet_NaN()) << ")" << std::endl;
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std::cout << "signaling nan = " << std::numeric_limits<half>::signaling_NaN() << " (0x" << std::hex
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<< numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::signaling_NaN()) << ")" << std::endl;
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VERIFY(NumTraits<half>::IsSigned);
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VERIFY_IS_EQUAL(numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::infinity()),
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numext::bit_cast<numext::uint16_t>(half(std::numeric_limits<float>::infinity())));
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// There is no guarantee that casting a 32-bit NaN to 16-bit has a precise
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// bit pattern. We test that it is in fact a NaN, then test the signaling
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// bit (msb of significand is 1 for quiet, 0 for signaling).
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const numext::uint16_t HALF_QUIET_BIT = 0x0200;
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VERIFY((numext::isnan)(std::numeric_limits<half>::quiet_NaN()) &&
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(numext::isnan)(half(std::numeric_limits<float>::quiet_NaN())) &&
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((numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::quiet_NaN()) & HALF_QUIET_BIT) > 0) &&
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((numext::bit_cast<numext::uint16_t>(half(std::numeric_limits<float>::quiet_NaN())) & HALF_QUIET_BIT) > 0));
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// After a cast to half, a signaling NaN may become non-signaling
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// (e.g. in the case of casting float to native __fp16). Thus, we check that
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// both are NaN, and that only the `numeric_limits` version is signaling.
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VERIFY((numext::isnan)(std::numeric_limits<half>::signaling_NaN()) &&
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(numext::isnan)(half(std::numeric_limits<float>::signaling_NaN())) &&
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((numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::signaling_NaN()) & HALF_QUIET_BIT) == 0));
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VERIFY((std::numeric_limits<half>::min)() > half(0.f));
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VERIFY((std::numeric_limits<half>::denorm_min)() > half(0.f));
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VERIFY((std::numeric_limits<half>::min)() / half(2) > half(0.f));
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VERIFY_IS_EQUAL((std::numeric_limits<half>::denorm_min)() / half(2), half(0.f));
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// Test to see that we are able to link against the symbols for digits and
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// digits10.
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volatile const int& digits10 = std::numeric_limits<half>::digits10;
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volatile const int& digits = std::numeric_limits<half>::digits;
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VERIFY((digits10) != (digits));
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}
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void test_arithmetic() {
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VERIFY_IS_EQUAL(float(half(2) + half(2)), 4);
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VERIFY_IS_EQUAL(float(half(2) + half(-2)), 0);
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VERIFY_IS_APPROX(float(half(0.33333f) + half(0.66667f)), 1.0f);
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VERIFY_IS_EQUAL(float(half(2.0f) * half(-5.5f)), -11.0f);
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VERIFY_IS_APPROX(float(half(1.0f) / half(3.0f)), 0.33333f);
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VERIFY_IS_EQUAL(float(-half(4096.0f)), -4096.0f);
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VERIFY_IS_EQUAL(float(-half(-4096.0f)), 4096.0f);
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half x(3);
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half y = ++x;
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VERIFY_IS_EQUAL(x, half(4));
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VERIFY_IS_EQUAL(y, half(4));
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y = --x;
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VERIFY_IS_EQUAL(x, half(3));
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VERIFY_IS_EQUAL(y, half(3));
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y = x++;
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VERIFY_IS_EQUAL(x, half(4));
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VERIFY_IS_EQUAL(y, half(3));
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y = x--;
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VERIFY_IS_EQUAL(x, half(3));
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VERIFY_IS_EQUAL(y, half(4));
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}
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void test_comparison() {
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VERIFY(half(1.0f) > half(0.5f));
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VERIFY(half(0.5f) < half(1.0f));
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VERIFY(!(half(1.0f) < half(0.5f)));
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VERIFY(!(half(0.5f) > half(1.0f)));
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VERIFY(!(half(4.0f) > half(4.0f)));
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VERIFY(!(half(4.0f) < half(4.0f)));
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VERIFY(!(half(0.0f) < half(-0.0f)));
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VERIFY(!(half(-0.0f) < half(0.0f)));
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VERIFY(!(half(0.0f) > half(-0.0f)));
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VERIFY(!(half(-0.0f) > half(0.0f)));
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VERIFY(half(0.2f) > half(-1.0f));
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VERIFY(half(-1.0f) < half(0.2f));
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VERIFY(half(-16.0f) < half(-15.0f));
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VERIFY(half(1.0f) == half(1.0f));
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VERIFY(half(1.0f) != half(2.0f));
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// Comparisons with NaNs and infinities.
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#if !EIGEN_COMP_MSVC
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// Visual Studio errors out on divisions by 0
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VERIFY(!(half(0.0 / 0.0) == half(0.0 / 0.0)));
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VERIFY(half(0.0 / 0.0) != half(0.0 / 0.0));
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VERIFY(!(half(1.0) == half(0.0 / 0.0)));
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VERIFY(!(half(1.0) < half(0.0 / 0.0)));
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VERIFY(!(half(1.0) > half(0.0 / 0.0)));
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VERIFY(half(1.0) != half(0.0 / 0.0));
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VERIFY(half(1.0) < half(1.0 / 0.0));
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VERIFY(half(1.0) > half(-1.0 / 0.0));
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#endif
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}
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void test_basic_functions() {
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constexpr float PI = static_cast<float>(EIGEN_PI);
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VERIFY_IS_EQUAL(float(numext::abs(half(3.5f))), 3.5f);
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VERIFY_IS_EQUAL(float(abs(half(3.5f))), 3.5f);
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VERIFY_IS_EQUAL(float(numext::abs(half(-3.5f))), 3.5f);
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VERIFY_IS_EQUAL(float(abs(half(-3.5f))), 3.5f);
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VERIFY_IS_EQUAL(float(numext::floor(half(3.5f))), 3.0f);
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VERIFY_IS_EQUAL(float(floor(half(3.5f))), 3.0f);
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VERIFY_IS_EQUAL(float(numext::floor(half(-3.5f))), -4.0f);
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VERIFY_IS_EQUAL(float(floor(half(-3.5f))), -4.0f);
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VERIFY_IS_EQUAL(float(numext::ceil(half(3.5f))), 4.0f);
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VERIFY_IS_EQUAL(float(ceil(half(3.5f))), 4.0f);
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VERIFY_IS_EQUAL(float(numext::ceil(half(-3.5f))), -3.0f);
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VERIFY_IS_EQUAL(float(ceil(half(-3.5f))), -3.0f);
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VERIFY_IS_APPROX(float(numext::sqrt(half(0.0f))), 0.0f);
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VERIFY_IS_APPROX(float(sqrt(half(0.0f))), 0.0f);
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VERIFY_IS_APPROX(float(numext::sqrt(half(4.0f))), 2.0f);
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VERIFY_IS_APPROX(float(sqrt(half(4.0f))), 2.0f);
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VERIFY_IS_APPROX(float(numext::pow(half(0.0f), half(1.0f))), 0.0f);
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VERIFY_IS_APPROX(float(pow(half(0.0f), half(1.0f))), 0.0f);
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VERIFY_IS_APPROX(float(numext::pow(half(2.0f), half(2.0f))), 4.0f);
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VERIFY_IS_APPROX(float(pow(half(2.0f), half(2.0f))), 4.0f);
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VERIFY_IS_EQUAL(float(numext::exp(half(0.0f))), 1.0f);
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VERIFY_IS_EQUAL(float(exp(half(0.0f))), 1.0f);
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VERIFY_IS_APPROX(float(numext::exp(half(PI))), 20.f + PI);
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VERIFY_IS_APPROX(float(exp(half(PI))), 20.f + PI);
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VERIFY_IS_EQUAL(float(numext::expm1(half(0.0f))), 0.0f);
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VERIFY_IS_EQUAL(float(expm1(half(0.0f))), 0.0f);
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VERIFY_IS_APPROX(float(numext::expm1(half(2.0f))), 6.3890561f);
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VERIFY_IS_APPROX(float(expm1(half(2.0f))), 6.3890561f);
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VERIFY_IS_EQUAL(float(numext::log(half(1.0f))), 0.0f);
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VERIFY_IS_EQUAL(float(log(half(1.0f))), 0.0f);
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VERIFY_IS_APPROX(float(numext::log(half(10.0f))), 2.30273f);
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VERIFY_IS_APPROX(float(log(half(10.0f))), 2.30273f);
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VERIFY_IS_EQUAL(float(numext::log1p(half(0.0f))), 0.0f);
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VERIFY_IS_EQUAL(float(log1p(half(0.0f))), 0.0f);
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VERIFY_IS_APPROX(float(numext::log1p(half(10.0f))), 2.3978953f);
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VERIFY_IS_APPROX(float(log1p(half(10.0f))), 2.3978953f);
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VERIFY_IS_APPROX(numext::fmod(half(5.3f), half(2.0f)), half(1.3f));
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VERIFY_IS_APPROX(fmod(half(5.3f), half(2.0f)), half(1.3f));
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VERIFY_IS_APPROX(numext::fmod(half(-18.5f), half(-4.2f)), half(-1.7f));
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VERIFY_IS_APPROX(fmod(half(-18.5f), half(-4.2f)), half(-1.7f));
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}
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void test_trigonometric_functions() {
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constexpr float PI = static_cast<float>(EIGEN_PI);
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VERIFY_IS_APPROX(numext::cos(half(0.0f)), half(cosf(0.0f)));
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VERIFY_IS_APPROX(cos(half(0.0f)), half(cosf(0.0f)));
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VERIFY_IS_APPROX(numext::cos(half(PI)), half(cosf(PI)));
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// VERIFY_IS_APPROX(numext::cos(half(PI/2)), half(cosf(PI/2)));
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// VERIFY_IS_APPROX(numext::cos(half(3*PI/2)), half(cosf(3*PI/2)));
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VERIFY_IS_APPROX(numext::cos(half(3.5f)), half(cosf(3.5f)));
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VERIFY_IS_APPROX(numext::sin(half(0.0f)), half(sinf(0.0f)));
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VERIFY_IS_APPROX(sin(half(0.0f)), half(sinf(0.0f)));
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// VERIFY_IS_APPROX(numext::sin(half(PI)), half(sinf(PI)));
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VERIFY_IS_APPROX(numext::sin(half(PI / 2)), half(sinf(PI / 2)));
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VERIFY_IS_APPROX(numext::sin(half(3 * PI / 2)), half(sinf(3 * PI / 2)));
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VERIFY_IS_APPROX(numext::sin(half(3.5f)), half(sinf(3.5f)));
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VERIFY_IS_APPROX(numext::tan(half(0.0f)), half(tanf(0.0f)));
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VERIFY_IS_APPROX(tan(half(0.0f)), half(tanf(0.0f)));
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// VERIFY_IS_APPROX(numext::tan(half(PI)), half(tanf(PI)));
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// VERIFY_IS_APPROX(numext::tan(half(PI/2)), half(tanf(PI/2)));
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// VERIFY_IS_APPROX(numext::tan(half(3*PI/2)), half(tanf(3*PI/2)));
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VERIFY_IS_APPROX(numext::tan(half(3.5f)), half(tanf(3.5f)));
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}
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void test_array() {
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typedef Array<half, 1, Dynamic> ArrayXh;
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Index size = internal::random<Index>(1, 10);
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Index i = internal::random<Index>(0, size - 1);
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ArrayXh a1 = ArrayXh::Random(size), a2 = ArrayXh::Random(size);
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VERIFY_IS_APPROX(a1 + a1, half(2) * a1);
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VERIFY((a1.abs() >= half(0)).all());
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VERIFY_IS_APPROX((a1 * a1).sqrt(), a1.abs());
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VERIFY(((a1.min)(a2) <= (a1.max)(a2)).all());
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a1(i) = half(-10.);
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VERIFY_IS_EQUAL(a1.minCoeff(), half(-10.));
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a1(i) = half(10.);
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VERIFY_IS_EQUAL(a1.maxCoeff(), half(10.));
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std::stringstream ss;
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ss << a1;
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}
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void test_product() {
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typedef Matrix<half, Dynamic, Dynamic> MatrixXh;
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Index rows = internal::random<Index>(1, EIGEN_TEST_MAX_SIZE);
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Index cols = internal::random<Index>(1, EIGEN_TEST_MAX_SIZE);
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Index depth = internal::random<Index>(1, EIGEN_TEST_MAX_SIZE);
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MatrixXh Ah = MatrixXh::Random(rows, depth);
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MatrixXh Bh = MatrixXh::Random(depth, cols);
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MatrixXh Ch = MatrixXh::Random(rows, cols);
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MatrixXf Af = Ah.cast<float>();
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|
MatrixXf Bf = Bh.cast<float>();
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|
MatrixXf Cf = Ch.cast<float>();
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|
VERIFY_IS_APPROX(Ch.noalias() += Ah * Bh, (Cf.noalias() += Af * Bf).cast<half>());
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|
}
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|
|
|
EIGEN_DECLARE_TEST(half_float) {
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CALL_SUBTEST(test_numtraits());
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|
for (int i = 0; i < g_repeat; i++) {
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|
CALL_SUBTEST(test_conversion());
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|
CALL_SUBTEST(test_arithmetic());
|
|
CALL_SUBTEST(test_comparison());
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|
CALL_SUBTEST(test_basic_functions());
|
|
CALL_SUBTEST(test_trigonometric_functions());
|
|
CALL_SUBTEST(test_array());
|
|
CALL_SUBTEST(test_product());
|
|
}
|
|
}
|