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Vectorize pow for integer base / exponent types

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This commit is contained in:
Charles Schlosser
2022-08-29 19:23:54 +00:00
committed by Rasmus Munk Larsen
parent 8acbf5c11c
commit e5af9f87f2
7 changed files with 134 additions and 8 deletions
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74
test/array_cwise.cpp
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@@ -126,6 +126,72 @@ void pow_test() {
VERIFY(all_pass);
}
template <typename Scalar, typename ScalarExponent>
Scalar calc_overflow_threshold(const ScalarExponent exponent) {
EIGEN_USING_STD(exp2);
EIGEN_STATIC_ASSERT((NumTraits<Scalar>::digits() < 2 * NumTraits<double>::digits()), BASE_TYPE_IS_TOO_BIG);
if (exponent < 2)
return NumTraits<Scalar>::highest();
else {
const double max_exponent = static_cast<double>(NumTraits<Scalar>::digits());
const double clamped_exponent = exponent < max_exponent ? static_cast<double>(exponent) : max_exponent;
const double threshold = exp2(max_exponent / clamped_exponent);
return static_cast<Scalar>(threshold);
}
}
template <typename Base, typename Exponent>
void test_exponent(Exponent exponent) {
EIGEN_USING_STD(pow);
const Base max_abs_bases = 10000;
// avoid integer overflow in Base type
Base threshold = calc_overflow_threshold<Base, Exponent>(numext::abs(exponent));
// avoid numbers that can't be verified with std::pow
double double_threshold = calc_overflow_threshold<double, Exponent>(numext::abs(exponent));
// use the lesser of these two thresholds
Base testing_threshold = threshold < double_threshold ? threshold : static_cast<Base>(double_threshold);
// avoid divide by zero
Base min_abs_base = exponent < 0 ? 1 : 0;
// avoid excessively long test
Base max_abs_base = numext::mini(testing_threshold, max_abs_bases);
// test both vectorized and non-vectorized code paths
const Index array_size = 2 * internal::packet_traits<Base>::size + 1;
Base max_base = numext::mini(testing_threshold, max_abs_bases);
Base min_base = NumTraits<Base>::IsSigned ? -max_base : 0;
ArrayX<Base> x(array_size), y(array_size);
bool all_pass = true;
for (Base base = min_base; base <= max_base; base++) {
if (exponent < 0 && base == 0) continue;
x.setConstant(base);
y = x.pow(exponent);
Base e = pow(base, exponent);
for (Base a : y) {
bool pass = a == e;
all_pass &= pass;
if (!pass) {
std::cout << "pow(" << base << "," << exponent << ") = " << a << " != " << e << std::endl;
}
}
}
VERIFY(all_pass);
}
template <typename Base, typename Exponent>
void int_pow_test() {
Exponent max_exponent = NumTraits<Base>::digits();
Exponent min_exponent = NumTraits<Exponent>::IsSigned ? -max_exponent : 0;
for (Exponent exponent = min_exponent; exponent < max_exponent; exponent++) {
test_exponent<Base, Exponent>(exponent);
}
}
template<typename ArrayType> void array(const ArrayType& m)
{
typedef typename ArrayType::Scalar Scalar;
@@ -500,6 +566,14 @@ template<typename ArrayType> void array_real(const ArrayType& m)
VERIFY_IS_APPROX(m3.pow(RealScalar(-2)), m3.square().inverse());
pow_test<Scalar>();
typedef typename internal::make_integer<Scalar>::type SignedInt;
typedef typename std::make_unsigned<SignedInt>::type UnsignedInt;
int_pow_test<SignedInt, SignedInt>();
int_pow_test<SignedInt, UnsignedInt>();
int_pow_test<UnsignedInt, SignedInt>();
int_pow_test<UnsignedInt, UnsignedInt>();
VERIFY_IS_APPROX(log10(m3), log(m3)/numext::log(Scalar(10)));
VERIFY_IS_APPROX(log2(m3), log(m3)/numext::log(Scalar(2)));