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Fix arm32 float division and related bugs

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This commit is contained in:
Charles Schlosser 2023-08-29 00:36:07 +00:00 committed by Rasmus Munk Larsen
parent 2873916f1c
commit 81b48065ea
4 changed files with 115 additions and 82 deletions
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158
Eigen/src/Core/arch/NEON/PacketMath.h
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@ -956,57 +956,6 @@ template<> EIGEN_STRONG_INLINE Packet2ul pmul<Packet2ul>(const Packet2ul& a, con
vdup_n_u64(vgetq_lane_u64(a, 1)*vgetq_lane_u64(b, 1)));
}
template<> EIGEN_STRONG_INLINE Packet2f pdiv<Packet2f>(const Packet2f& a, const Packet2f& b)
{
#if EIGEN_ARCH_ARM64
return vdiv_f32(a,b);
#else
Packet2f inv, restep, div;
// NEON does not offer a divide instruction, we have to do a reciprocal approximation
// However NEON in contrast to other SIMD engines (AltiVec/SSE), offers
// a reciprocal estimate AND a reciprocal step -which saves a few instructions
// vrecpeq_f32() returns an estimate to 1/b, which we will finetune with
// Newton-Raphson and vrecpsq_f32()
inv = vrecpe_f32(b);
// This returns a differential, by which we will have to multiply inv to get a better
// approximation of 1/b.
restep = vrecps_f32(b, inv);
inv = vmul_f32(restep, inv);
// Finally, multiply a by 1/b and get the wanted result of the division.
div = vmul_f32(a, inv);
return div;
#endif
}
template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)
{
#if EIGEN_ARCH_ARM64
return vdivq_f32(a,b);
#else
Packet4f inv, restep, div;
// NEON does not offer a divide instruction, we have to do a reciprocal approximation
// However NEON in contrast to other SIMD engines (AltiVec/SSE), offers
// a reciprocal estimate AND a reciprocal step -which saves a few instructions
// vrecpeq_f32() returns an estimate to 1/b, which we will finetune with
// Newton-Raphson and vrecpsq_f32()
inv = vrecpeq_f32(b);
// This returns a differential, by which we will have to multiply inv to get a better
// approximation of 1/b.
restep = vrecpsq_f32(b, inv);
inv = vmulq_f32(restep, inv);
// Finally, multiply a by 1/b and get the wanted result of the division.
div = vmulq_f32(a, inv);
return div;
#endif
}
template<> EIGEN_STRONG_INLINE Packet4c pdiv<Packet4c>(const Packet4c& /*a*/, const Packet4c& /*b*/)
{
eigen_assert(false && "packet integer division are not supported by NEON");
@ -3362,26 +3311,115 @@ template<> EIGEN_STRONG_INLINE Packet4ui psqrt(const Packet4ui& a) {
return res;
}
EIGEN_STRONG_INLINE Packet4f prsqrt_float_unsafe(const Packet4f& a) {
// Compute approximate reciprocal sqrt.
// Does not correctly handle +/- 0 or +inf
float32x4_t result = vrsqrteq_f32(a);
result = vmulq_f32(vrsqrtsq_f32(vmulq_f32(a, result), result), result);
result = vmulq_f32(vrsqrtsq_f32(vmulq_f32(a, result), result), result);
return result;
}
EIGEN_STRONG_INLINE Packet2f prsqrt_float_unsafe(const Packet2f& a) {
// Compute approximate reciprocal sqrt.
// Does not correctly handle +/- 0 or +inf
float32x2_t result = vrsqrte_f32(a);
result = vmul_f32(vrsqrts_f32(vmul_f32(a, result), result), result);
result = vmul_f32(vrsqrts_f32(vmul_f32(a, result), result), result);
return result;
}
template<typename Packet> Packet prsqrt_float_common(const Packet& a) {
const Packet cst_zero = pzero(a);
const Packet cst_inf = pset1<Packet>(NumTraits<float>::infinity());
Packet return_zero = pcmp_eq(a, cst_inf);
Packet return_inf = pcmp_eq(a, cst_zero);
Packet result = prsqrt_float_unsafe(a);
result = pselect(return_inf, por(cst_inf, a), result);
result = pandnot(result, return_zero);
return result;
}
template<> EIGEN_STRONG_INLINE Packet4f prsqrt(const Packet4f& a) {
// Do Newton iterations for 1/sqrt(x).
return generic_rsqrt_newton_step<Packet4f, /*Steps=*/2>::run(a, vrsqrteq_f32(a));
return prsqrt_float_common(a);
}
template<> EIGEN_STRONG_INLINE Packet2f prsqrt(const Packet2f& a) {
// Compute approximate reciprocal sqrt.
return generic_rsqrt_newton_step<Packet2f, /*Steps=*/2>::run(a, vrsqrte_f32(a));
return prsqrt_float_common(a);
}
template<> EIGEN_STRONG_INLINE Packet4f preciprocal<Packet4f>(const Packet4f& a)
{
// Compute approximate reciprocal.
float32x4_t result = vrecpeq_f32(a);
result = vmulq_f32(vrecpsq_f32(a, result), result);
result = vmulq_f32(vrecpsq_f32(a, result), result);
return result;
}
template<> EIGEN_STRONG_INLINE Packet2f preciprocal<Packet2f>(const Packet2f& a)
{
// Compute approximate reciprocal.
float32x2_t result = vrecpe_f32(a);
result = vmul_f32(vrecps_f32(a, result), result);
result = vmul_f32(vrecps_f32(a, result), result);
return result;
}
// Unfortunately vsqrt_f32 is only available for A64.
#if EIGEN_ARCH_ARM64
template<> EIGEN_STRONG_INLINE Packet4f psqrt(const Packet4f& _x){return vsqrtq_f32(_x);}
template<> EIGEN_STRONG_INLINE Packet2f psqrt(const Packet2f& _x){return vsqrt_f32(_x); }
template<> EIGEN_STRONG_INLINE Packet4f psqrt(const Packet4f& a) { return vsqrtq_f32(a); }
template<> EIGEN_STRONG_INLINE Packet2f psqrt(const Packet2f& a) { return vsqrt_f32(a); }
template<> EIGEN_STRONG_INLINE Packet4f pdiv(const Packet4f& a, const Packet4f& b) { return vdivq_f32(a, b); }
template<> EIGEN_STRONG_INLINE Packet2f pdiv(const Packet2f& a, const Packet2f& b) { return vdiv_f32(a, b); }
#else
template<> EIGEN_STRONG_INLINE Packet4f psqrt(const Packet4f& a) {
return generic_sqrt_newton_step<Packet4f>::run(a, prsqrt(a));
template<typename Packet>
EIGEN_STRONG_INLINE Packet psqrt_float_common(const Packet& a) {
const Packet cst_zero = pzero(a);
const Packet cst_inf = pset1<Packet>(NumTraits<float>::infinity());
Packet result = pmul(a, prsqrt_float_unsafe(a));
Packet a_is_zero = pcmp_eq(a, cst_zero);
Packet a_is_inf = pcmp_eq(a, cst_inf);
Packet return_a = por(a_is_zero, a_is_inf);
result = pselect(return_a, a, result);
return result;
}
template<> EIGEN_STRONG_INLINE Packet4f psqrt(const Packet4f& a) {
return psqrt_float_common(a);
}
template<> EIGEN_STRONG_INLINE Packet2f psqrt(const Packet2f& a) {
return generic_sqrt_newton_step<Packet2f>::run(a, prsqrt(a));
return psqrt_float_common(a);
}
template<typename Packet>
EIGEN_STRONG_INLINE Packet pdiv_float_common(const Packet& a, const Packet& b) {
// if b is large, NEON intrinsics will flush preciprocal(b) to zero
// avoid underflow with the following manipulation:
// a / b = f * (a * reciprocal(f * b))
const Packet cst_one = pset1<Packet>(1.0f);
const Packet cst_quarter = pset1<Packet>(0.25f);
const Packet cst_thresh = pset1<Packet>(NumTraits<float>::highest() / 4.0f);
Packet b_will_underflow = pcmp_le(cst_thresh, pabs(b));
Packet f = pselect(b_will_underflow, cst_quarter, cst_one);
Packet result = pmul(f, pmul(a, preciprocal(pmul(b, f))));
return result;
}
template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b) {
return pdiv_float_common(a, b);
}
template<> EIGEN_STRONG_INLINE Packet2f pdiv<Packet2f>(const Packet2f& a, const Packet2f& b) {
return pdiv_float_common(a, b);
}
#endif

16
test/array_cwise.cpp
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@ -47,7 +47,7 @@ std::vector<Scalar> special_values() {
const Scalar sqrt2 = Scalar(std::sqrt(2));
const Scalar inf = Eigen::NumTraits<Scalar>::infinity();
const Scalar nan = Eigen::NumTraits<Scalar>::quiet_NaN();
const Scalar denorm_min = std::numeric_limits<Scalar>::denorm_min();
const Scalar denorm_min = EIGEN_ARCH_ARM ? zero : std::numeric_limits<Scalar>::denorm_min();
const Scalar min = (std::numeric_limits<Scalar>::min)();
const Scalar max = (std::numeric_limits<Scalar>::max)();
const Scalar max_exp = (static_cast<Scalar>(int(Eigen::NumTraits<Scalar>::max_exponent())) * Scalar(EIGEN_LN2)) / eps;
@ -97,6 +97,12 @@ void binary_op_test(std::string name, Fn fun, RefFn ref) {
for (Index j = 0; j < lhs.cols(); ++j) {
Scalar e = static_cast<Scalar>(ref(lhs(i,j), rhs(i,j)));
Scalar a = actual(i, j);
#if EIGEN_ARCH_ARM
// Work around NEON flush-to-zero mode
// if ref returns denormalized value and Eigen returns 0, then skip the test
int ref_fpclass = std::fpclassify(e);
if (a == Scalar(0) && ref_fpclass == FP_SUBNORMAL) continue;
#endif
bool success = (a==e) || ((numext::isfinite)(e) && internal::isApprox(a, e, tol)) || ((numext::isnan)(a) && (numext::isnan)(e));
if ((a == a) && (e == e)) success &= (bool)numext::signbit(e) == (bool)numext::signbit(a);
all_pass &= success;
@ -767,7 +773,12 @@ template<typename ArrayType> void array_real(const ArrayType& m)
m3(rows, cols),
m4 = m1;
m4 = (m4.abs()==Scalar(0)).select(Scalar(1),m4);
// avoid denormalized values so verification doesn't fail on platforms that don't support them
// denormalized behavior is tested elsewhere (unary_op_test, binary_ops_test)
const Scalar min = (std::numeric_limits<Scalar>::min)();
m1 = (m1.abs()<min).select(Scalar(0),m1);
m2 = (m2.abs()<min).select(Scalar(0),m2);
m4 = (m4.abs()<min).select(Scalar(1),m4);
Scalar s1 = internal::random<Scalar>();
@ -808,6 +819,7 @@ template<typename ArrayType> void array_real(const ArrayType& m)
// avoid inf and NaNs so verification doesn't fail
m3 = m4.abs();
VERIFY_IS_APPROX(m3.sqrt(), sqrt(abs(m3)));
VERIFY_IS_APPROX(m3.rsqrt(), Scalar(1)/sqrt(abs(m3)));
VERIFY_IS_APPROX(rsqrt(m3), Scalar(1)/sqrt(abs(m3)));

4
test/packetmath.cpp
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@ -754,7 +754,7 @@ void packetmath_test_IEEE_corner_cases(const RefFunctorT& ref_fun,
}
// Test for subnormals.
if (Cond && std::numeric_limits<Scalar>::has_denorm == std::denorm_present) {
if (Cond && std::numeric_limits<Scalar>::has_denorm == std::denorm_present && !EIGEN_ARCH_ARM) {
for (int scale = 1; scale < 5; ++scale) {
// When EIGEN_FAST_MATH is 1 we relax the conditions slightly, and allow the function
@ -912,12 +912,14 @@ void packetmath_real() {
CHECK_CWISE1_BYREF1_IF(PacketTraits::HasExp, REF_FREXP, internal::pfrexp);
if (PacketTraits::HasExp) {
// Check denormals:
#if !EIGEN_ARCH_ARM
for (int j=0; j<3; ++j) {
data1[0] = Scalar(std::ldexp(1, NumTraits<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);
}
#endif
// zero
data1[0] = Scalar(0);

19
test/sparse_permutations.cpp
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@ -113,25 +113,6 @@ template<int OtherStorage, typename SparseMatrixType> void sparse_permutations(c
res_d = p.inverse()*mat_d;
VERIFY(res.isApprox(res_d) && "inv(p)*mat");
// test non-plaintype expressions that require additional temporary
const Scalar alpha(2.34);
res_d = p * (alpha * mat_d);
VERIFY_TEMPORARY_COUNT( res = p * (alpha * mat), 2);
VERIFY( res.isApprox(res_d) && "p*(alpha*mat)" );
res_d = (alpha * mat_d) * p;
VERIFY_TEMPORARY_COUNT( res = (alpha * mat) * p, 2);
VERIFY( res.isApprox(res_d) && "(alpha*mat)*p" );
res_d = p.inverse() * (alpha * mat_d);
VERIFY_TEMPORARY_COUNT( res = p.inverse() * (alpha * mat), 2);
VERIFY( res.isApprox(res_d) && "inv(p)*(alpha*mat)" );
res_d = (alpha * mat_d) * p.inverse();
VERIFY_TEMPORARY_COUNT( res = (alpha * mat) * p.inverse(), 2);
VERIFY( res.isApprox(res_d) && "(alpha*mat)*inv(p)" );
//
VERIFY( is_sorted( (p * mat * p.inverse()).eval() ));