From 81b48065ea673cd352d11ef9b6a3d86778ac962d Mon Sep 17 00:00:00 2001 From: Charles Schlosser Date: Tue, 29 Aug 2023 00:36:07 +0000 Subject: [PATCH] Fix arm32 float division and related bugs --- Eigen/src/Core/arch/NEON/PacketMath.h | 158 ++++++++++++++++---------- test/array_cwise.cpp | 16 ++- test/packetmath.cpp | 4 +- test/sparse_permutations.cpp | 19 ---- 4 files changed, 115 insertions(+), 82 deletions(-) diff --git a/Eigen/src/Core/arch/NEON/PacketMath.h b/Eigen/src/Core/arch/NEON/PacketMath.h index adb1342b4..e70f8b0e2 100644 --- a/Eigen/src/Core/arch/NEON/PacketMath.h +++ b/Eigen/src/Core/arch/NEON/PacketMath.h @@ -956,57 +956,6 @@ template<> EIGEN_STRONG_INLINE Packet2ul pmul(const Packet2ul& a, con vdup_n_u64(vgetq_lane_u64(a, 1)*vgetq_lane_u64(b, 1))); } -template<> EIGEN_STRONG_INLINE Packet2f pdiv(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(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(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 Packet prsqrt_float_common(const Packet& a) { + const Packet cst_zero = pzero(a); + const Packet cst_inf = pset1(NumTraits::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::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::run(a, vrsqrte_f32(a)); + return prsqrt_float_common(a); +} + +template<> EIGEN_STRONG_INLINE Packet4f preciprocal(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(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::run(a, prsqrt(a)); +template +EIGEN_STRONG_INLINE Packet psqrt_float_common(const Packet& a) { + const Packet cst_zero = pzero(a); + const Packet cst_inf = pset1(NumTraits::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::run(a, prsqrt(a)); + return psqrt_float_common(a); +} + +template +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(1.0f); + const Packet cst_quarter = pset1(0.25f); + const Packet cst_thresh = pset1(NumTraits::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(const Packet4f& a, const Packet4f& b) { + return pdiv_float_common(a, b); +} + +template<> EIGEN_STRONG_INLINE Packet2f pdiv(const Packet2f& a, const Packet2f& b) { + return pdiv_float_common(a, b); } #endif diff --git a/test/array_cwise.cpp b/test/array_cwise.cpp index 49e667252..058b721fa 100644 --- a/test/array_cwise.cpp +++ b/test/array_cwise.cpp @@ -47,7 +47,7 @@ std::vector special_values() { const Scalar sqrt2 = Scalar(std::sqrt(2)); const Scalar inf = Eigen::NumTraits::infinity(); const Scalar nan = Eigen::NumTraits::quiet_NaN(); - const Scalar denorm_min = std::numeric_limits::denorm_min(); + const Scalar denorm_min = EIGEN_ARCH_ARM ? zero : std::numeric_limits::denorm_min(); const Scalar min = (std::numeric_limits::min)(); const Scalar max = (std::numeric_limits::max)(); const Scalar max_exp = (static_cast(int(Eigen::NumTraits::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(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 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::min)(); + m1 = (m1.abs()(); @@ -808,6 +819,7 @@ template 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))); diff --git a/test/packetmath.cpp b/test/packetmath.cpp index 5dd4cbc3d..b5b040187 100644 --- a/test/packetmath.cpp +++ b/test/packetmath.cpp @@ -754,7 +754,7 @@ void packetmath_test_IEEE_corner_cases(const RefFunctorT& ref_fun, } // Test for subnormals. - if (Cond && std::numeric_limits::has_denorm == std::denorm_present) { + if (Cond && std::numeric_limits::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::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); diff --git a/test/sparse_permutations.cpp b/test/sparse_permutations.cpp index 775c5608b..3e46bfa35 100644 --- a/test/sparse_permutations.cpp +++ b/test/sparse_permutations.cpp @@ -113,25 +113,6 @@ template 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() ));