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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "main.h"
template<typename T, typename U>
bool check_if_equal_or_nans(const T& actual, const U& expected) {
return ((actual == expected) || ((numext::isnan)(actual) && (numext::isnan)(expected)));
}
template<typename T, typename U>
bool check_if_equal_or_nans(const std::complex<T>& actual, const std::complex<U>& expected) {
return check_if_equal_or_nans(numext::real(actual), numext::real(expected))
&& check_if_equal_or_nans(numext::imag(actual), numext::imag(expected));
}
template<typename T, typename U>
bool test_is_equal_or_nans(const T& actual, const U& expected)
{
if (check_if_equal_or_nans(actual, expected)) {
return true;
}
// false:
std::cerr
<< "\n actual = " << actual
<< "\n expected = " << expected << "\n\n";
return false;
}
#define VERIFY_IS_EQUAL_OR_NANS(a, b) VERIFY(test_is_equal_or_nans(a, b))
template<typename T>
void check_abs() {
typedef typename NumTraits<T>::Real Real;
Real zero(0);
if(NumTraits<T>::IsSigned)
VERIFY_IS_EQUAL(numext::abs(-T(1)), T(1));
VERIFY_IS_EQUAL(numext::abs(T(0)), T(0));
VERIFY_IS_EQUAL(numext::abs(T(1)), T(1));
for(int k=0; k<100; ++k)
{
T x = internal::random<T>();
if(!internal::is_same<T,bool>::value)
x = x/Real(2);
if(NumTraits<T>::IsSigned)
{
VERIFY_IS_EQUAL(numext::abs(x), numext::abs(-x));
VERIFY( numext::abs(-x) >= zero );
}
VERIFY( numext::abs(x) >= zero );
VERIFY_IS_APPROX( numext::abs2(x), numext::abs2(numext::abs(x)) );
}
}
template<typename T>
void check_arg() {
typedef typename NumTraits<T>::Real Real;
VERIFY_IS_EQUAL(numext::abs(T(0)), T(0));
VERIFY_IS_EQUAL(numext::abs(T(1)), T(1));
for(int k=0; k<100; ++k)
{
T x = internal::random<T>();
Real y = numext::arg(x);
VERIFY_IS_APPROX( y, std::arg(x) );
}
}
template<typename T>
struct check_sqrt_impl {
static void run() {
for (int i=0; i<1000; ++i) {
const T x = numext::abs(internal::random<T>());
const T sqrtx = numext::sqrt(x);
VERIFY_IS_APPROX(sqrtx*sqrtx, x);
}
// Corner cases.
const T zero = T(0);
const T one = T(1);
const T inf = std::numeric_limits<T>::infinity();
const T nan = std::numeric_limits<T>::quiet_NaN();
VERIFY_IS_EQUAL(numext::sqrt(zero), zero);
VERIFY_IS_EQUAL(numext::sqrt(inf), inf);
VERIFY((numext::isnan)(numext::sqrt(nan)));
VERIFY((numext::isnan)(numext::sqrt(-one)));
}
};
template<typename T>
struct check_sqrt_impl<std::complex<T> > {
static void run() {
typedef typename std::complex<T> ComplexT;
for (int i=0; i<1000; ++i) {
const ComplexT x = internal::random<ComplexT>();
const ComplexT sqrtx = numext::sqrt(x);
VERIFY_IS_APPROX(sqrtx*sqrtx, x);
}
// Corner cases.
const T zero = T(0);
const T one = T(1);
const T inf = std::numeric_limits<T>::infinity();
const T nan = std::numeric_limits<T>::quiet_NaN();
// Set of corner cases from https://en.cppreference.com/w/cpp/numeric/complex/sqrt
const int kNumCorners = 20;
const ComplexT corners[kNumCorners][2] = {
{ComplexT(zero, zero), ComplexT(zero, zero)},
{ComplexT(-zero, zero), ComplexT(zero, zero)},
{ComplexT(zero, -zero), ComplexT(zero, zero)},
{ComplexT(-zero, -zero), ComplexT(zero, zero)},
{ComplexT(one, inf), ComplexT(inf, inf)},
{ComplexT(nan, inf), ComplexT(inf, inf)},
{ComplexT(one, -inf), ComplexT(inf, -inf)},
{ComplexT(nan, -inf), ComplexT(inf, -inf)},
{ComplexT(-inf, one), ComplexT(zero, inf)},
{ComplexT(inf, one), ComplexT(inf, zero)},
{ComplexT(-inf, -one), ComplexT(zero, -inf)},
{ComplexT(inf, -one), ComplexT(inf, -zero)},
{ComplexT(-inf, nan), ComplexT(nan, inf)},
{ComplexT(inf, nan), ComplexT(inf, nan)},
{ComplexT(zero, nan), ComplexT(nan, nan)},
{ComplexT(one, nan), ComplexT(nan, nan)},
{ComplexT(nan, zero), ComplexT(nan, nan)},
{ComplexT(nan, one), ComplexT(nan, nan)},
{ComplexT(nan, -one), ComplexT(nan, nan)},
{ComplexT(nan, nan), ComplexT(nan, nan)},
};
for (int i=0; i<kNumCorners; ++i) {
const ComplexT& x = corners[i][0];
const ComplexT sqrtx = corners[i][1];
VERIFY_IS_EQUAL_OR_NANS(numext::sqrt(x), sqrtx);
}
}
};
template<typename T>
void check_sqrt() {
check_sqrt_impl<T>::run();
}
template<typename T>
struct check_rsqrt_impl {
static void run() {
const T zero = T(0);
const T one = T(1);
const T inf = std::numeric_limits<T>::infinity();
const T nan = std::numeric_limits<T>::quiet_NaN();
for (int i=0; i<1000; ++i) {
const T x = numext::abs(internal::random<T>());
const T rsqrtx = numext::rsqrt(x);
const T invx = one / x;
VERIFY_IS_APPROX(rsqrtx*rsqrtx, invx);
}
// Corner cases.
VERIFY_IS_EQUAL(numext::rsqrt(zero), inf);
VERIFY_IS_EQUAL(numext::rsqrt(inf), zero);
VERIFY((numext::isnan)(numext::rsqrt(nan)));
VERIFY((numext::isnan)(numext::rsqrt(-one)));
}
};
template<typename T>
struct check_rsqrt_impl<std::complex<T> > {
static void run() {
typedef typename std::complex<T> ComplexT;
const T zero = T(0);
const T one = T(1);
const T inf = std::numeric_limits<T>::infinity();
const T nan = std::numeric_limits<T>::quiet_NaN();
for (int i=0; i<1000; ++i) {
const ComplexT x = internal::random<ComplexT>();
const ComplexT invx = ComplexT(one, zero) / x;
const ComplexT rsqrtx = numext::rsqrt(x);
VERIFY_IS_APPROX(rsqrtx*rsqrtx, invx);
}
// GCC and MSVC differ in their treatment of 1/(0 + 0i)
// GCC/clang = (inf, nan)
// MSVC = (nan, nan)
// and 1 / (x + inf i)
// GCC/clang = (0, 0)
// MSVC = (nan, nan)
#if (EIGEN_COMP_GNUC)
{
const int kNumCorners = 20;
const ComplexT corners[kNumCorners][2] = {
// Only consistent across GCC, clang
{ComplexT(zero, zero), ComplexT(zero, zero)},
{ComplexT(-zero, zero), ComplexT(zero, zero)},
{ComplexT(zero, -zero), ComplexT(zero, zero)},
{ComplexT(-zero, -zero), ComplexT(zero, zero)},
{ComplexT(one, inf), ComplexT(inf, inf)},
{ComplexT(nan, inf), ComplexT(inf, inf)},
{ComplexT(one, -inf), ComplexT(inf, -inf)},
{ComplexT(nan, -inf), ComplexT(inf, -inf)},
// Consistent across GCC, clang, MSVC
{ComplexT(-inf, one), ComplexT(zero, inf)},
{ComplexT(inf, one), ComplexT(inf, zero)},
{ComplexT(-inf, -one), ComplexT(zero, -inf)},
{ComplexT(inf, -one), ComplexT(inf, -zero)},
{ComplexT(-inf, nan), ComplexT(nan, inf)},
{ComplexT(inf, nan), ComplexT(inf, nan)},
{ComplexT(zero, nan), ComplexT(nan, nan)},
{ComplexT(one, nan), ComplexT(nan, nan)},
{ComplexT(nan, zero), ComplexT(nan, nan)},
{ComplexT(nan, one), ComplexT(nan, nan)},
{ComplexT(nan, -one), ComplexT(nan, nan)},
{ComplexT(nan, nan), ComplexT(nan, nan)},
};
for (int i=0; i<kNumCorners; ++i) {
const ComplexT& x = corners[i][0];
const ComplexT rsqrtx = ComplexT(one, zero) / corners[i][1];
VERIFY_IS_EQUAL_OR_NANS(numext::rsqrt(x), rsqrtx);
}
}
#endif
}
};
template<typename T>
void check_rsqrt() {
check_rsqrt_impl<T>::run();
}
EIGEN_DECLARE_TEST(numext) {
for(int k=0; k<g_repeat; ++k)
{
CALL_SUBTEST( check_abs<bool>() );
CALL_SUBTEST( check_abs<signed char>() );
CALL_SUBTEST( check_abs<unsigned char>() );
CALL_SUBTEST( check_abs<short>() );
CALL_SUBTEST( check_abs<unsigned short>() );
CALL_SUBTEST( check_abs<int>() );
CALL_SUBTEST( check_abs<unsigned int>() );
CALL_SUBTEST( check_abs<long>() );
CALL_SUBTEST( check_abs<unsigned long>() );
CALL_SUBTEST( check_abs<half>() );
CALL_SUBTEST( check_abs<bfloat16>() );
CALL_SUBTEST( check_abs<float>() );
CALL_SUBTEST( check_abs<double>() );
CALL_SUBTEST( check_abs<long double>() );
CALL_SUBTEST( check_abs<std::complex<float> >() );
CALL_SUBTEST( check_abs<std::complex<double> >() );
CALL_SUBTEST( check_arg<std::complex<float> >() );
CALL_SUBTEST( check_arg<std::complex<double> >() );
CALL_SUBTEST( check_sqrt<float>() );
CALL_SUBTEST( check_sqrt<double>() );
CALL_SUBTEST( check_sqrt<std::complex<float> >() );
CALL_SUBTEST( check_sqrt<std::complex<double> >() );
CALL_SUBTEST( check_rsqrt<float>() );
CALL_SUBTEST( check_rsqrt<double>() );
CALL_SUBTEST( check_rsqrt<std::complex<float> >() );
CALL_SUBTEST( check_rsqrt<std::complex<double> >() );
}
}
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