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packetmath.cpp
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// 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 "packetmath_test_shared.h"
#include "random_without_cast_overflow.h"
template <typename T>
inline T REF_ADD(const T& a, const T& b) {
return a + b;
}
template <typename T>
inline T REF_SUB(const T& a, const T& b) {
return a - b;
}
template <typename T>
inline T REF_MUL(const T& a, const T& b) {
return a * b;
}
template <typename T>
inline T REF_DIV(const T& a, const T& b) {
return a / b;
}
template <typename T>
inline T REF_ABS_DIFF(const T& a, const T& b) {
return a > b ? a - b : b - a;
}
// Specializations for bool.
template <>
inline bool REF_ADD(const bool& a, const bool& b) {
return a || b;
}
template <>
inline bool REF_SUB(const bool& a, const bool& b) {
return a ^ b;
}
template <>
inline bool REF_MUL(const bool& a, const bool& b) {
return a && b;
}
template <typename T>
inline T REF_FREXP(const T& x, T& exp) {
int iexp;
EIGEN_USING_STD(frexp)
const T out = static_cast<T>(frexp(x, &iexp));
exp = static_cast<T>(iexp);
return out;
}
template <typename T>
inline T REF_LDEXP(const T& x, const T& exp) {
EIGEN_USING_STD(ldexp)
return static_cast<T>(ldexp(x, static_cast<int>(exp)));
}
// Uses pcast to cast from one array to another.
template <typename SrcPacket, typename TgtPacket, int SrcCoeffRatio,
int TgtCoeffRatio>
struct pcast_array;
template <typename SrcPacket, typename TgtPacket, int TgtCoeffRatio>
struct pcast_array<SrcPacket, TgtPacket, 1, TgtCoeffRatio> {
typedef typename internal::unpacket_traits<SrcPacket>::type SrcScalar;
typedef typename internal::unpacket_traits<TgtPacket>::type TgtScalar;
static void cast(const SrcScalar* src, size_t size, TgtScalar* dst) {
static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
size_t i;
for (i = 0; i < size && i + SrcPacketSize <= size; i += TgtPacketSize) {
internal::pstoreu(dst + i, internal::pcast<SrcPacket, TgtPacket>(
internal::ploadu<SrcPacket>(src + i)));
}
// Leftovers that cannot be loaded into a packet.
for (; i < size; ++i) {
dst[i] = static_cast<TgtScalar>(src[i]);
}
}
};
template <typename SrcPacket, typename TgtPacket>
struct pcast_array<SrcPacket, TgtPacket, 2, 1> {
static void cast(
const typename internal::unpacket_traits<SrcPacket>::type* src,
size_t size, typename internal::unpacket_traits<TgtPacket>::type* dst) {
static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
for (size_t i = 0; i < size; i += TgtPacketSize) {
SrcPacket a = internal::ploadu<SrcPacket>(src + i);
SrcPacket b = internal::ploadu<SrcPacket>(src + i + SrcPacketSize);
internal::pstoreu(dst + i, internal::pcast<SrcPacket, TgtPacket>(a, b));
}
}
};
template <typename SrcPacket, typename TgtPacket>
struct pcast_array<SrcPacket, TgtPacket, 4, 1> {
static void cast(
const typename internal::unpacket_traits<SrcPacket>::type* src,
size_t size, typename internal::unpacket_traits<TgtPacket>::type* dst) {
static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
for (size_t i = 0; i < size; i += TgtPacketSize) {
SrcPacket a = internal::ploadu<SrcPacket>(src + i);
SrcPacket b = internal::ploadu<SrcPacket>(src + i + SrcPacketSize);
SrcPacket c = internal::ploadu<SrcPacket>(src + i + 2 * SrcPacketSize);
SrcPacket d = internal::ploadu<SrcPacket>(src + i + 3 * SrcPacketSize);
internal::pstoreu(dst + i,
internal::pcast<SrcPacket, TgtPacket>(a, b, c, d));
}
}
};
template <typename SrcPacket, typename TgtPacket>
struct pcast_array<SrcPacket, TgtPacket, 8, 1> {
static void cast(
const typename internal::unpacket_traits<SrcPacket>::type* src,
size_t size, typename internal::unpacket_traits<TgtPacket>::type* dst) {
static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
for (size_t i = 0; i < size; i += TgtPacketSize) {
SrcPacket a = internal::ploadu<SrcPacket>(src + i);
SrcPacket b = internal::ploadu<SrcPacket>(src + i + SrcPacketSize);
SrcPacket c = internal::ploadu<SrcPacket>(src + i + 2 * SrcPacketSize);
SrcPacket d = internal::ploadu<SrcPacket>(src + i + 3 * SrcPacketSize);
SrcPacket e = internal::ploadu<SrcPacket>(src + i + 4 * SrcPacketSize);
SrcPacket f = internal::ploadu<SrcPacket>(src + i + 5 * SrcPacketSize);
SrcPacket g = internal::ploadu<SrcPacket>(src + i + 6 * SrcPacketSize);
SrcPacket h = internal::ploadu<SrcPacket>(src + i + 7 * SrcPacketSize);
internal::pstoreu(dst + i, internal::pcast<SrcPacket, TgtPacket>(
a, b, c, d, e, f, g, h));
}
}
};
template <typename SrcPacket, typename TgtPacket, int SrcCoeffRatio,
int TgtCoeffRatio, bool CanCast = false>
struct test_cast_helper;
template <typename SrcPacket, typename TgtPacket, int SrcCoeffRatio,
int TgtCoeffRatio>
struct test_cast_helper<SrcPacket, TgtPacket, SrcCoeffRatio, TgtCoeffRatio,
false> {
static void run() {}
};
template <typename SrcPacket, typename TgtPacket, int SrcCoeffRatio,
int TgtCoeffRatio>
struct test_cast_helper<SrcPacket, TgtPacket, SrcCoeffRatio, TgtCoeffRatio,
true> {
static void run() {
typedef typename internal::unpacket_traits<SrcPacket>::type SrcScalar;
typedef typename internal::unpacket_traits<TgtPacket>::type TgtScalar;
static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
static const int BlockSize = SrcPacketSize * SrcCoeffRatio;
eigen_assert(BlockSize == TgtPacketSize * TgtCoeffRatio &&
"Packet sizes and cast ratios are mismatched.");
static const int DataSize = 10 * BlockSize;
EIGEN_ALIGN_MAX SrcScalar data1[DataSize];
EIGEN_ALIGN_MAX TgtScalar data2[DataSize];
EIGEN_ALIGN_MAX TgtScalar ref[DataSize];
// Construct a packet of scalars that will not overflow when casting
for (int i = 0; i < DataSize; ++i) {
data1[i] =
internal::random_without_cast_overflow<SrcScalar, TgtScalar>::value();
}
for (int i = 0; i < DataSize; ++i) {
ref[i] = static_cast<const TgtScalar>(data1[i]);
}
pcast_array<SrcPacket, TgtPacket, SrcCoeffRatio, TgtCoeffRatio>::cast(
data1, DataSize, data2);
VERIFY(test::areApprox(ref, data2, DataSize) && "internal::pcast<>");
}
};
template <typename SrcPacket, typename TgtPacket>
struct test_cast {
static void run() {
typedef typename internal::unpacket_traits<SrcPacket>::type SrcScalar;
typedef typename internal::unpacket_traits<TgtPacket>::type TgtScalar;
typedef typename internal::type_casting_traits<SrcScalar, TgtScalar>
TypeCastingTraits;
static const int SrcCoeffRatio = TypeCastingTraits::SrcCoeffRatio;
static const int TgtCoeffRatio = TypeCastingTraits::TgtCoeffRatio;
static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
static const bool HasCast =
internal::unpacket_traits<SrcPacket>::vectorizable &&
internal::unpacket_traits<TgtPacket>::vectorizable &&
TypeCastingTraits::VectorizedCast &&
(SrcPacketSize * SrcCoeffRatio == TgtPacketSize * TgtCoeffRatio);
test_cast_helper<SrcPacket, TgtPacket, SrcCoeffRatio, TgtCoeffRatio,
HasCast>::run();
}
};
template <
typename SrcPacket, typename TgtScalar,
typename TgtPacket = typename internal::packet_traits<TgtScalar>::type,
bool Vectorized = internal::packet_traits<TgtScalar>::Vectorizable,
bool HasHalf = !internal::is_same<
typename internal::unpacket_traits<TgtPacket>::half, TgtPacket>::value>
struct test_cast_runner;
template <typename SrcPacket, typename TgtScalar, typename TgtPacket>
struct test_cast_runner<SrcPacket, TgtScalar, TgtPacket, true, false> {
static void run() { test_cast<SrcPacket, TgtPacket>::run(); }
};
template <typename SrcPacket, typename TgtScalar, typename TgtPacket>
struct test_cast_runner<SrcPacket, TgtScalar, TgtPacket, true, true> {
static void run() {
test_cast<SrcPacket, TgtPacket>::run();
test_cast_runner<SrcPacket, TgtScalar, typename internal::unpacket_traits<
TgtPacket>::half>::run();
}
};
template <typename SrcPacket, typename TgtScalar, typename TgtPacket>
struct test_cast_runner<SrcPacket, TgtScalar, TgtPacket, false, false> {
static void run() {}
};
template <typename Scalar, typename Packet, typename EnableIf = void>
struct packetmath_pcast_ops_runner {
static void run() {
test_cast_runner<Packet, float>::run();
test_cast_runner<Packet, double>::run();
test_cast_runner<Packet, int8_t>::run();
test_cast_runner<Packet, uint8_t>::run();
test_cast_runner<Packet, int16_t>::run();
test_cast_runner<Packet, uint16_t>::run();
test_cast_runner<Packet, int32_t>::run();
test_cast_runner<Packet, uint32_t>::run();
test_cast_runner<Packet, int64_t>::run();
test_cast_runner<Packet, uint64_t>::run();
test_cast_runner<Packet, bool>::run();
test_cast_runner<Packet, std::complex<float> >::run();
test_cast_runner<Packet, std::complex<double> >::run();
test_cast_runner<Packet, half>::run();
test_cast_runner<Packet, bfloat16>::run();
}
};
// Only some types support cast from std::complex<>.
template <typename Scalar, typename Packet>
struct packetmath_pcast_ops_runner<
Scalar, Packet,
typename internal::enable_if<NumTraits<Scalar>::IsComplex>::type> {
static void run() {
test_cast_runner<Packet, std::complex<float> >::run();
test_cast_runner<Packet, std::complex<double> >::run();
test_cast_runner<Packet, half>::run();
test_cast_runner<Packet, bfloat16>::run();
}
};
template <typename Scalar, typename Packet>
void packetmath_boolean_mask_ops() {
const int PacketSize = internal::unpacket_traits<Packet>::size;
const int size = 2 * PacketSize;
EIGEN_ALIGN_MAX Scalar data1[size];
EIGEN_ALIGN_MAX Scalar data2[size];
EIGEN_ALIGN_MAX Scalar ref[size];
for (int i = 0; i < size; ++i) {
data1[i] = internal::random<Scalar>();
}
CHECK_CWISE1(internal::ptrue, internal::ptrue);
CHECK_CWISE2_IF(true, internal::pandnot, internal::pandnot);
for (int i = 0; i < PacketSize; ++i) {
data1[i] = Scalar(i);
data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
}
CHECK_CWISE2_IF(true, internal::pcmp_eq, internal::pcmp_eq);
// Test (-0) == (0) for signed operations
for (int i = 0; i < PacketSize; ++i) {
data1[i] = Scalar(-0.0);
data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
}
CHECK_CWISE2_IF(true, internal::pcmp_eq, internal::pcmp_eq);
// Test NaN
for (int i = 0; i < PacketSize; ++i) {
data1[i] = std::numeric_limits<Scalar>::quiet_NaN();
data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
}
CHECK_CWISE2_IF(true, internal::pcmp_eq, internal::pcmp_eq);
}
// Packet16b representing bool does not support ptrue, pandnot or pcmp_eq, since
// the scalar path
// (for some compilers) compute the bitwise and with 0x1 of the results to keep
// the value in [0,1].
template <>
void packetmath_boolean_mask_ops<bool, internal::packet_traits<bool>::type>() {}
template <typename Scalar, typename Packet>
void packetmath_minus_zero_add() {
const int PacketSize = internal::unpacket_traits<Packet>::size;
const int size = 2 * PacketSize;
EIGEN_ALIGN_MAX Scalar data1[size];
EIGEN_ALIGN_MAX Scalar data2[size];
EIGEN_ALIGN_MAX Scalar ref[size];
for (int i = 0; i < PacketSize; ++i) {
data1[i] = Scalar(-0.0);
data1[i + PacketSize] = Scalar(-0.0);
}
CHECK_CWISE2_IF(internal::packet_traits<Scalar>::HasAdd, REF_ADD,
internal::padd);
}
// Ensure optimization barrier compiles and doesn't modify contents.
// Only applies to raw types, so will not work for std::complex, Eigen::half
// or Eigen::bfloat16. For those you would need to refer to an underlying
// storage element.
template <typename Packet, typename EnableIf = void>
struct eigen_optimization_barrier_test {
static void run() {}
};
template <typename Packet>
struct eigen_optimization_barrier_test<
Packet, typename internal::enable_if<
!NumTraits<Packet>::IsComplex &&
!internal::is_same<Packet, Eigen::half>::value &&
!internal::is_same<Packet, Eigen::bfloat16>::value>::type> {
static void run() {
typedef typename internal::unpacket_traits<Packet>::type Scalar;
Scalar s = internal::random<Scalar>();
Packet barrier = internal::pset1<Packet>(s);
EIGEN_OPTIMIZATION_BARRIER(barrier);
eigen_assert(s == internal::pfirst(barrier) &&
"EIGEN_OPTIMIZATION_BARRIER");
}
};
template <typename Scalar, typename Packet>
void packetmath() {
typedef internal::packet_traits<Scalar> PacketTraits;
const int PacketSize = internal::unpacket_traits<Packet>::size;
typedef typename NumTraits<Scalar>::Real RealScalar;
if (g_first_pass)
std::cerr << "=== Testing packet of type '" << typeid(Packet).name()
<< "' and scalar type '" << typeid(Scalar).name()
<< "' and size '" << PacketSize << "' ===\n";
const int max_size = PacketSize > 4 ? PacketSize : 4;
const int size = PacketSize * max_size;
EIGEN_ALIGN_MAX Scalar data1[size];
EIGEN_ALIGN_MAX Scalar data2[size];
EIGEN_ALIGN_MAX Scalar data3[size];
EIGEN_ALIGN_MAX Scalar ref[size];
RealScalar refvalue = RealScalar(0);
eigen_optimization_barrier_test<Packet>::run();
eigen_optimization_barrier_test<Scalar>::run();
for (int i = 0; i < size; ++i) {
data1[i] = internal::random<Scalar>() / RealScalar(PacketSize);
data2[i] = internal::random<Scalar>() / RealScalar(PacketSize);
refvalue = (std::max)(refvalue, numext::abs(data1[i]));
}
internal::pstore(data2, internal::pload<Packet>(data1));
VERIFY(test::areApprox(data1, data2, PacketSize) && "aligned load/store");
for (int offset = 0; offset < PacketSize; ++offset) {
internal::pstore(data2, internal::ploadu<Packet>(data1 + offset));
VERIFY(test::areApprox(data1 + offset, data2, PacketSize) &&
"internal::ploadu");
}
for (int offset = 0; offset < PacketSize; ++offset) {
internal::pstoreu(data2 + offset, internal::pload<Packet>(data1));
VERIFY(test::areApprox(data1, data2 + offset, PacketSize) &&
"internal::pstoreu");
}
if (internal::unpacket_traits<Packet>::masked_load_available) {
test::packet_helper<
internal::unpacket_traits<Packet>::masked_load_available, Packet>
h;
unsigned long long max_umask = (0x1ull << PacketSize);
for (int offset = 0; offset < PacketSize; ++offset) {
for (unsigned long long umask = 0; umask < max_umask; ++umask) {
h.store(data2, h.load(data1 + offset, umask));
for (int k = 0; k < PacketSize; ++k)
data3[k] =
((umask & (0x1ull << k)) >> k) ? data1[k + offset] : Scalar(0);
VERIFY(test::areApprox(data3, data2, PacketSize) &&
"internal::ploadu masked");
}
}
}
if (internal::unpacket_traits<Packet>::masked_store_available) {
test::packet_helper<
internal::unpacket_traits<Packet>::masked_store_available, Packet>
h;
unsigned long long max_umask = (0x1ull << PacketSize);
for (int offset = 0; offset < PacketSize; ++offset) {
for (unsigned long long umask = 0; umask < max_umask; ++umask) {
internal::pstore(data2, internal::pset1<Packet>(Scalar(0)));
h.store(data2, h.loadu(data1 + offset), umask);
for (int k = 0; k < PacketSize; ++k)
data3[k] =
((umask & (0x1ull << k)) >> k) ? data1[k + offset] : Scalar(0);
VERIFY(test::areApprox(data3, data2, PacketSize) &&
"internal::pstoreu masked");
}
}
}
VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasAdd);
VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasSub);
VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasMul);
CHECK_CWISE2_IF(PacketTraits::HasAdd, REF_ADD, internal::padd);
CHECK_CWISE2_IF(PacketTraits::HasSub, REF_SUB, internal::psub);
CHECK_CWISE2_IF(PacketTraits::HasMul, REF_MUL, internal::pmul);
CHECK_CWISE2_IF(PacketTraits::HasDiv, REF_DIV, internal::pdiv);
if (PacketTraits::HasNegate)
CHECK_CWISE1(internal::negate, internal::pnegate);
CHECK_CWISE1(numext::conj, internal::pconj);
for (int offset = 0; offset < 3; ++offset) {
for (int i = 0; i < PacketSize; ++i) ref[i] = data1[offset];
internal::pstore(data2, internal::pset1<Packet>(data1[offset]));
VERIFY(test::areApprox(ref, data2, PacketSize) && "internal::pset1");
}
{
for (int i = 0; i < PacketSize * 4; ++i) ref[i] = data1[i / PacketSize];
Packet A0, A1, A2, A3;
internal::pbroadcast4<Packet>(data1, A0, A1, A2, A3);
internal::pstore(data2 + 0 * PacketSize, A0);
internal::pstore(data2 + 1 * PacketSize, A1);
internal::pstore(data2 + 2 * PacketSize, A2);
internal::pstore(data2 + 3 * PacketSize, A3);
VERIFY(test::areApprox(ref, data2, 4 * PacketSize) &&
"internal::pbroadcast4");
}
{
for (int i = 0; i < PacketSize * 2; ++i) ref[i] = data1[i / PacketSize];
Packet A0, A1;
internal::pbroadcast2<Packet>(data1, A0, A1);
internal::pstore(data2 + 0 * PacketSize, A0);
internal::pstore(data2 + 1 * PacketSize, A1);
VERIFY(test::areApprox(ref, data2, 2 * PacketSize) &&
"internal::pbroadcast2");
}
VERIFY(internal::isApprox(data1[0],
internal::pfirst(internal::pload<Packet>(data1))) &&
"internal::pfirst");
if (PacketSize > 1) {
// apply different offsets to check that ploaddup is robust to unaligned
// inputs
for (int offset = 0; offset < 4; ++offset) {
for (int i = 0; i < PacketSize / 2; ++i)
ref[2 * i + 0] = ref[2 * i + 1] = data1[offset + i];
internal::pstore(data2, internal::ploaddup<Packet>(data1 + offset));
VERIFY(test::areApprox(ref, data2, PacketSize) && "ploaddup");
}
}
if (PacketSize > 2) {
// apply different offsets to check that ploadquad is robust to unaligned
// inputs
for (int offset = 0; offset < 4; ++offset) {
for (int i = 0; i < PacketSize / 4; ++i)
ref[4 * i + 0] = ref[4 * i + 1] = ref[4 * i + 2] = ref[4 * i + 3] =
data1[offset + i];
internal::pstore(data2, internal::ploadquad<Packet>(data1 + offset));
VERIFY(test::areApprox(ref, data2, PacketSize) && "ploadquad");
}
}
ref[0] = Scalar(0);
for (int i = 0; i < PacketSize; ++i) ref[0] += data1[i];
VERIFY(test::isApproxAbs(ref[0],
internal::predux(internal::pload<Packet>(data1)),
refvalue) &&
"internal::predux");
if (PacketSize == 8 &&
internal::unpacket_traits<
typename internal::unpacket_traits<Packet>::half>::size ==
4) // so far, predux_half_downto4 is only required in such a case
{
int HalfPacketSize = PacketSize > 4 ? PacketSize / 2 : PacketSize;
for (int i = 0; i < HalfPacketSize; ++i) ref[i] = Scalar(0);
for (int i = 0; i < PacketSize; ++i) ref[i % HalfPacketSize] += data1[i];
internal::pstore(
data2, internal::predux_half_dowto4(internal::pload<Packet>(data1)));
VERIFY(test::areApprox(ref, data2, HalfPacketSize) &&
"internal::predux_half_dowto4");
}
ref[0] = Scalar(1);
for (int i = 0; i < PacketSize; ++i) ref[0] = REF_MUL(ref[0], data1[i]);
VERIFY(internal::isApprox(
ref[0], internal::predux_mul(internal::pload<Packet>(data1))) &&
"internal::predux_mul");
for (int i = 0; i < PacketSize; ++i) ref[i] = data1[PacketSize - i - 1];
internal::pstore(data2, internal::preverse(internal::pload<Packet>(data1)));
VERIFY(test::areApprox(ref, data2, PacketSize) && "internal::preverse");
internal::PacketBlock<Packet> kernel;
for (int i = 0; i < PacketSize; ++i) {
kernel.packet[i] = internal::pload<Packet>(data1 + i * PacketSize);
}
ptranspose(kernel);
for (int i = 0; i < PacketSize; ++i) {
internal::pstore(data2, kernel.packet[i]);
for (int j = 0; j < PacketSize; ++j) {
VERIFY(test::isApproxAbs(data2[j], data1[i + j * PacketSize], refvalue) &&
"ptranspose");
}
}
if (PacketTraits::HasBlend) {
Packet thenPacket = internal::pload<Packet>(data1);
Packet elsePacket = internal::pload<Packet>(data2);
EIGEN_ALIGN_MAX internal::Selector<PacketSize> selector;
for (int i = 0; i < PacketSize; ++i) {
selector.select[i] = i;
}
Packet blend = internal::pblend(selector, thenPacket, elsePacket);
EIGEN_ALIGN_MAX Scalar result[size];
internal::pstore(result, blend);
for (int i = 0; i < PacketSize; ++i) {
VERIFY(test::isApproxAbs(
result[i], (selector.select[i] ? data1[i] : data2[i]), refvalue));
}
}
{
for (int i = 0; i < PacketSize; ++i) {
// "if" mask
unsigned char v = internal::random<bool>() ? 0xff : 0;
char* bytes = (char*)(data1 + i);
for (int k = 0; k < int(sizeof(Scalar)); ++k) {
bytes[k] = v;
}
// "then" packet
data1[i + PacketSize] = internal::random<Scalar>();
// "else" packet
data1[i + 2 * PacketSize] = internal::random<Scalar>();
}
CHECK_CWISE3_IF(true, internal::pselect, internal::pselect);
}
for (int i = 0; i < size; ++i) {
data1[i] = internal::random<Scalar>();
}
CHECK_CWISE1(internal::pzero, internal::pzero);
CHECK_CWISE2_IF(true, internal::por, internal::por);
CHECK_CWISE2_IF(true, internal::pxor, internal::pxor);
CHECK_CWISE2_IF(true, internal::pand, internal::pand);
packetmath_boolean_mask_ops<Scalar, Packet>();
packetmath_pcast_ops_runner<Scalar, Packet>::run();
packetmath_minus_zero_add<Scalar, Packet>();
for (int i = 0; i < size; ++i) {
data1[i] = numext::abs(internal::random<Scalar>());
}
CHECK_CWISE1_IF(PacketTraits::HasSqrt, numext::sqrt, internal::psqrt);
CHECK_CWISE1_IF(PacketTraits::HasRsqrt, numext::rsqrt, internal::prsqrt);
}
// Notice that this definition works for complex types as well.
// c++11 has std::log2 for real, but not for complex types.
template <typename Scalar>
Scalar log2(Scalar x) {
return Scalar(EIGEN_LOG2E) * std::log(x);
}
template <typename Scalar, typename Packet>
void packetmath_real() {
typedef internal::packet_traits<Scalar> PacketTraits;
const int PacketSize = internal::unpacket_traits<Packet>::size;
const int size = PacketSize * 4;
EIGEN_ALIGN_MAX Scalar data1[PacketSize * 4];
EIGEN_ALIGN_MAX Scalar data2[PacketSize * 4];
EIGEN_ALIGN_MAX Scalar ref[PacketSize * 4];
for (int i = 0; i < size; ++i) {
data1[i] = Scalar(internal::random<double>(0, 1) *
std::pow(10., internal::random<double>(-6, 6)));
data2[i] = Scalar(internal::random<double>(0, 1) *
std::pow(10., internal::random<double>(-6, 6)));
}
if (internal::random<float>(0, 1) < 0.1f)
data1[internal::random<int>(0, PacketSize)] = Scalar(0);
CHECK_CWISE1_IF(PacketTraits::HasLog, std::log, internal::plog);
CHECK_CWISE1_IF(PacketTraits::HasLog, log2, internal::plog2);
CHECK_CWISE1_IF(PacketTraits::HasRsqrt, numext::rsqrt, internal::prsqrt);
for (int i = 0; i < size; ++i) {
data1[i] = Scalar(internal::random<double>(-1, 1) *
std::pow(10., internal::random<double>(-3, 3)));
data2[i] = Scalar(internal::random<double>(-1, 1) *
std::pow(10., internal::random<double>(-3, 3)));
}
CHECK_CWISE1_IF(PacketTraits::HasSin, std::sin, internal::psin);
CHECK_CWISE1_IF(PacketTraits::HasCos, std::cos, internal::pcos);
CHECK_CWISE1_IF(PacketTraits::HasTan, std::tan, internal::ptan);
CHECK_CWISE1_EXACT_IF(PacketTraits::HasRound, numext::round,
internal::pround);
CHECK_CWISE1_EXACT_IF(PacketTraits::HasCeil, numext::ceil, internal::pceil);
CHECK_CWISE1_EXACT_IF(PacketTraits::HasFloor, numext::floor,
internal::pfloor);
CHECK_CWISE1_EXACT_IF(PacketTraits::HasRint, numext::rint, internal::print);
// Rounding edge cases.
if (PacketTraits::HasRound || PacketTraits::HasCeil ||
PacketTraits::HasFloor || PacketTraits::HasRint) {
typedef typename internal::make_integer<Scalar>::type IntType;
// Start with values that cannot fit inside an integer, work down to less
// than one.
Scalar val = numext::mini(
Scalar(2) * static_cast<Scalar>(NumTraits<IntType>::highest()),
NumTraits<Scalar>::highest());
std::vector<Scalar> values;
while (val > Scalar(0.25)) {
// Cover both even and odd, positive and negative cases.
values.push_back(val);
values.push_back(val + Scalar(0.3));
values.push_back(val + Scalar(0.5));
values.push_back(val + Scalar(0.8));
values.push_back(val + Scalar(1));
values.push_back(val + Scalar(1.3));
values.push_back(val + Scalar(1.5));
values.push_back(val + Scalar(1.8));
values.push_back(-val);
values.push_back(-val - Scalar(0.3));
values.push_back(-val - Scalar(0.5));
values.push_back(-val - Scalar(0.8));
values.push_back(-val - Scalar(1));
values.push_back(-val - Scalar(1.3));
values.push_back(-val - Scalar(1.5));
values.push_back(-val - Scalar(1.8));
values.push_back(Scalar(-1.5) + val); // Bug 1785.
val = val / Scalar(2);
}
values.push_back(NumTraits<Scalar>::infinity());
values.push_back(-NumTraits<Scalar>::infinity());
values.push_back(NumTraits<Scalar>::quiet_NaN());
for (size_t k = 0; k < values.size(); ++k) {
data1[0] = values[k];
CHECK_CWISE1_EXACT_IF(PacketTraits::HasRound, numext::round,
internal::pround);
CHECK_CWISE1_EXACT_IF(PacketTraits::HasCeil, numext::ceil,
internal::pceil);
CHECK_CWISE1_EXACT_IF(PacketTraits::HasFloor, numext::floor,
internal::pfloor);
CHECK_CWISE1_EXACT_IF(PacketTraits::HasRint, numext::rint,
internal::print);
}
}
for (int i = 0; i < size; ++i) {
data1[i] = Scalar(internal::random<double>(-1, 1));
data2[i] = Scalar(internal::random<double>(-1, 1));
}
CHECK_CWISE1_IF(PacketTraits::HasASin, std::asin, internal::pasin);
CHECK_CWISE1_IF(PacketTraits::HasACos, std::acos, internal::pacos);
for (int i = 0; i < size; ++i) {
data1[i] = Scalar(internal::random<double>(-87, 88));
data2[i] = Scalar(internal::random<double>(-87, 88));
}
CHECK_CWISE1_IF(PacketTraits::HasExp, std::exp, internal::pexp);
CHECK_CWISE1_BYREF1_IF(PacketTraits::HasExp, REF_FREXP, internal::pfrexp);
if (PacketTraits::HasExp) {
// Check denormals:
for (int j = 0; j < 3; ++j) {
data1[0] =
Scalar(std::ldexp(1, std::numeric_limits<Scalar>::min_exponent - j));
CHECK_CWISE1_BYREF1_IF(PacketTraits::HasExp, REF_FREXP, internal::pfrexp);
data1[0] = -data1[0];
CHECK_CWISE1_BYREF1_IF(PacketTraits::HasExp, REF_FREXP, internal::pfrexp);
}
// zero
data1[0] = Scalar(0);
CHECK_CWISE1_BYREF1_IF(PacketTraits::HasExp, REF_FREXP, internal::pfrexp);
// inf and NaN only compare output fraction, not exponent.
test::packet_helper<PacketTraits::HasExp, Packet> h;
Packet pout;
Scalar sout;
Scalar special[] = {NumTraits<Scalar>::infinity(),
-NumTraits<Scalar>::infinity(),
NumTraits<Scalar>::quiet_NaN()};
for (int i = 0; i < 3; ++i) {
data1[0] = special[i];
ref[0] = Scalar(REF_FREXP(data1[0], ref[PacketSize]));
h.store(data2,
internal::pfrexp(h.load(data1), h.forward_reference(pout, sout)));
VERIFY(test::areApprox(ref, data2, 1) && "internal::pfrexp");
}
}
for (int i = 0; i < PacketSize; ++i) {
data1[i] = Scalar(internal::random<double>(-1, 1));
data2[i] = Scalar(internal::random<double>(-1, 1));
}
for (int i = 0; i < PacketSize; ++i) {
data1[i + PacketSize] = Scalar(internal::random<int>(-4, 4));
data2[i + PacketSize] = Scalar(internal::random<double>(-4, 4));
}
CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
if (PacketTraits::HasExp) {
data1[0] = Scalar(-1);
// underflow to zero
data1[PacketSize] = Scalar(std::numeric_limits<Scalar>::min_exponent - 55);
CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
// overflow to inf
data1[PacketSize] = Scalar(std::numeric_limits<Scalar>::max_exponent + 10);
CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
// NaN stays NaN
data1[0] = NumTraits<Scalar>::quiet_NaN();
CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
VERIFY((numext::isnan)(data2[0]));
// inf stays inf
data1[0] = NumTraits<Scalar>::infinity();
data1[PacketSize] = Scalar(std::numeric_limits<Scalar>::min_exponent - 10);
CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
// zero stays zero
data1[0] = Scalar(0);
data1[PacketSize] = Scalar(std::numeric_limits<Scalar>::max_exponent + 10);
CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
// Small number big exponent.
data1[0] = Scalar(
std::ldexp(Scalar(1.0), std::numeric_limits<Scalar>::min_exponent - 1));
data1[PacketSize] = Scalar(-std::numeric_limits<Scalar>::min_exponent +
std::numeric_limits<Scalar>::max_exponent);
CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
// Big number small exponent.
data1[0] = Scalar(
std::ldexp(Scalar(1.0), std::numeric_limits<Scalar>::max_exponent - 1));
data1[PacketSize] = Scalar(+std::numeric_limits<Scalar>::min_exponent -
std::numeric_limits<Scalar>::max_exponent);
CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
}
for (int i = 0; i < size; ++i) {
data1[i] = Scalar(internal::random<double>(-1, 1) *
std::pow(10., internal::random<double>(-6, 6)));
data2[i] = Scalar(internal::random<double>(-1, 1) *
std::pow(10., internal::random<double>(-6, 6)));
}
data1[0] = Scalar(1e-20);
CHECK_CWISE1_IF(PacketTraits::HasTanh, std::tanh, internal::ptanh);
if (PacketTraits::HasExp && PacketSize >= 2) {
const Scalar small = std::numeric_limits<Scalar>::epsilon();
data1[0] = std::numeric_limits<Scalar>::quiet_NaN();
data1[1] = small;
test::packet_helper<PacketTraits::HasExp, Packet> h;
h.store(data2, internal::pexp(h.load(data1)));
VERIFY((numext::isnan)(data2[0]));
// TODO(rmlarsen): Re-enable for bfloat16.
if (!internal::is_same<Scalar, bfloat16>::value) {
VERIFY_IS_APPROX(std::exp(small), data2[1]);
}
data1[0] = -small;
data1[1] = Scalar(0);
h.store(data2, internal::pexp(h.load(data1)));
// TODO(rmlarsen): Re-enable for bfloat16.
if (!internal::is_same<Scalar, bfloat16>::value) {
VERIFY_IS_APPROX(std::exp(-small), data2[0]);
}
VERIFY_IS_EQUAL(std::exp(Scalar(0)), data2[1]);
data1[0] = (std::numeric_limits<Scalar>::min)();
data1[1] = -(std::numeric_limits<Scalar>::min)();
h.store(data2, internal::pexp(h.load(data1)));
VERIFY_IS_APPROX(std::exp((std::numeric_limits<Scalar>::min)()), data2[0]);
VERIFY_IS_APPROX(std::exp(-(std::numeric_limits<Scalar>::min)()), data2[1]);
data1[0] = std::numeric_limits<Scalar>::denorm_min();
data1[1] = -std::numeric_limits<Scalar>::denorm_min();
h.store(data2, internal::pexp(h.load(data1)));
VERIFY_IS_APPROX(std::exp(std::numeric_limits<Scalar>::denorm_min()),
data2[0]);
VERIFY_IS_APPROX(std::exp(-std::numeric_limits<Scalar>::denorm_min()),
data2[1]);
}
if (PacketTraits::HasTanh) {
// NOTE this test migh fail with GCC prior to 6.3, see MathFunctionsImpl.h
// for details.
data1[0] = std::numeric_limits<Scalar>::quiet_NaN();
test::packet_helper<internal::packet_traits<Scalar>::HasTanh, Packet> h;
h.store(data2, internal::ptanh(h.load(data1)));
VERIFY((numext::isnan)(data2[0]));
}
if (PacketTraits::HasExp) {
internal::scalar_logistic_op<Scalar> logistic;
for (int i = 0; i < size; ++i) {
data1[i] = Scalar(internal::random<double>(-20, 20));
}
test::packet_helper<PacketTraits::HasExp, Packet> h;
h.store(data2, logistic.packetOp(h.load(data1)));
for (int i = 0; i < PacketSize; ++i) {
VERIFY_IS_APPROX(data2[i], logistic(data1[i]));
}
}
#if EIGEN_HAS_C99_MATH && (EIGEN_COMP_CXXVER >= 11)
data1[0] = std::numeric_limits<Scalar>::infinity();
data1[1] = Scalar(-1);
CHECK_CWISE1_IF(PacketTraits::HasLog1p, std::log1p, internal::plog1p);
data1[0] = std::numeric_limits<Scalar>::infinity();
data1[1] = -std::numeric_limits<Scalar>::infinity();
CHECK_CWISE1_IF(PacketTraits::HasExpm1, std::expm1, internal::pexpm1);
#endif
if (PacketSize >= 2) {
data1[0] = std::numeric_limits<Scalar>::quiet_NaN();
data1[1] = std::numeric_limits<Scalar>::epsilon();
if (PacketTraits::HasLog) {
test::packet_helper<PacketTraits::HasLog, Packet> h;
h.store(data2, internal::plog(h.load(data1)));
VERIFY((numext::isnan)(data2[0]));
// TODO(cantonios): Re-enable for bfloat16.
if (!internal::is_same<Scalar, bfloat16>::value) {
VERIFY_IS_APPROX(std::log(data1[1]), data2[1]);
}
data1[0] = -std::numeric_limits<Scalar>::epsilon();
data1[1] = Scalar(0);
h.store(data2, internal::plog(h.load(data1)));
VERIFY((numext::isnan)(data2[0]));
VERIFY_IS_EQUAL(std::log(Scalar(0)), data2[1]);
data1[0] = (std::numeric_limits<Scalar>::min)();
data1[1] = -(std::numeric_limits<Scalar>::min)();
h.store(data2, internal::plog(h.load(data1)));
// TODO(cantonios): Re-enable for bfloat16.
if (!internal::is_same<Scalar, bfloat16>::value) {
VERIFY_IS_APPROX(std::log((std::numeric_limits<Scalar>::min)()),
data2[0]);
}
VERIFY((numext::isnan)(data2[1]));
// Note: 32-bit arm always flushes denorms to zero.
#if !EIGEN_ARCH_ARM
if (std::numeric_limits<Scalar>::has_denorm == std::denorm_present) {
data1[0] = std::numeric_limits<Scalar>::denorm_min();
data1[1] = -std::numeric_limits<Scalar>::denorm_min();
h.store(data2, internal::plog(h.load(data1)));
// TODO(rmlarsen): Reenable.
// VERIFY_IS_EQUAL(std::log(std::numeric_limits<Scalar>::denorm_min()),
// data2[0]);
VERIFY((numext::isnan)(data2[1]));
}
#endif
data1[0] = Scalar(-1.0f);
h.store(data2, internal::plog(h.load(data1)));
VERIFY((numext::isnan)(data2[0]));
data1[0] = std::numeric_limits<Scalar>::infinity();
h.store(data2, internal::plog(h.load(data1)));
VERIFY((numext::isinf)(data2[0]));
}
if (PacketTraits::HasLog1p) {
test::packet_helper<PacketTraits::HasLog1p, Packet> h;
data1[0] = Scalar(-2);
data1[1] = -std::numeric_limits<Scalar>::infinity();
h.store(data2, internal::plog1p(h.load(data1)));
VERIFY((numext::isnan)(data2[0]));
VERIFY((numext::isnan)(data2[1]));
}
if (PacketTraits::HasSqrt) {
test::packet_helper<PacketTraits::HasSqrt, Packet> h;
data1[0] = Scalar(-1.0f);
if (std::numeric_limits<Scalar>::has_denorm == std::denorm_present) {
data1[1] = -std::numeric_limits<Scalar>::denorm_min();
} else {
data1[1] = -std::numeric_limits<Scalar>::epsilon();
}
h.store(data2, internal::psqrt(h.load(data1)));
VERIFY((numext::isnan)(data2[0]));
VERIFY((numext::isnan)(data2[1]));
}
// TODO(rmlarsen): Re-enable for half and bfloat16.
if (PacketTraits::HasCos && !internal::is_same<Scalar, half>::value &&
!internal::is_same<Scalar, bfloat16>::value) {
test::packet_helper<PacketTraits::HasCos, Packet> h;
for (Scalar k = Scalar(1);
k < Scalar(10000) / std::numeric_limits<Scalar>::epsilon();
k *= Scalar(2)) {
for (int k1 = 0; k1 <= 1; ++k1) {
data1[0] = Scalar((2 * double(k) + k1) * double(EIGEN_PI) / 2 *
internal::random<double>(0.8, 1.2));
data1[1] = Scalar((2 * double(k) + 2 + k1) * double(EIGEN_PI) / 2 *
internal::random<double>(0.8, 1.2));
h.store(data2, internal::pcos(h.load(data1)));
h.store(data2 + PacketSize, internal::psin(h.load(data1)));
VERIFY(data2[0] <= Scalar(1.) && data2[0] >= Scalar(-1.));
VERIFY(data2[1] <= Scalar(1.) && data2[1] >= Scalar(-1.));
VERIFY(data2[PacketSize + 0] <= Scalar(1.) &&
data2[PacketSize + 0] >= Scalar(-1.));
VERIFY(data2[PacketSize + 1] <= Scalar(1.) &&
data2[PacketSize + 1] >= Scalar(-1.));
VERIFY_IS_APPROX(data2[0], std::cos(data1[0]));
VERIFY_IS_APPROX(data2[1], std::cos(data1[1]));
VERIFY_IS_APPROX(data2[PacketSize + 0], std::sin(data1[0]));
VERIFY_IS_APPROX(data2[PacketSize + 1], std::sin(data1[1]));
VERIFY_IS_APPROX(
numext::abs2(data2[0]) + numext::abs2(data2[PacketSize + 0]),
Scalar(1));
VERIFY_IS_APPROX(
numext::abs2(data2[1]) + numext::abs2(data2[PacketSize + 1]),
Scalar(1));
}
}
data1[0] = std::numeric_limits<Scalar>::infinity();
data1[1] = -std::numeric_limits<Scalar>::infinity();
h.store(data2, internal::psin(h.load(data1)));
VERIFY((numext::isnan)(data2[0]));
VERIFY((numext::isnan)(data2[1]));
h.store(data2, internal::pcos(h.load(data1)));
VERIFY((numext::isnan)(data2[0]));
VERIFY((numext::isnan)(data2[1]));
data1[0] = std::numeric_limits<Scalar>::quiet_NaN();
h.store(data2, internal::psin(h.load(data1)));
VERIFY((numext::isnan)(data2[0]));
h.store(data2, internal::pcos(h.load(data1)));
VERIFY((numext::isnan)(data2[0]));
data1[0] = -Scalar(0.);
h.store(data2, internal::psin(h.load(data1)));
VERIFY(internal::biteq(data2[0], data1[0]));
h.store(data2, internal::pcos(h.load(data1)));
VERIFY_IS_EQUAL(data2[0], Scalar(1));
}
}
}
#define CAST_CHECK_CWISE1_IF(COND, REFOP, POP, SCALAR, REFTYPE) \
if (COND) { \
test::packet_helper<COND, Packet> h; \
for (int i = 0; i < PacketSize; ++i) \
ref[i] = SCALAR(REFOP(static_cast<REFTYPE>(data1[i]))); \
h.store(data2, POP(h.load(data1))); \
VERIFY(test::areApprox(ref, data2, PacketSize) && #POP); \
}
template <typename Scalar>
Scalar propagate_nan_max(const Scalar& a, const Scalar& b) {
if ((numext::isnan)(a)) return a;
if ((numext::isnan)(b)) return b;
return (numext::maxi)(a, b);
}