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Vectorize pow(x, y). This closes https://gitlab.com/libeigen/eigen/-/issues/2085, which also contains a description of the algorithm.

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I ran some testing (comparing to `std::pow(double(x), double(y)))` for `x` in the set of all (positive) floats in the interval `[std::sqrt(std::numeric_limits<float>::min()), std::sqrt(std::numeric_limits<float>::max())]`, and `y` in `{2, sqrt(2), -sqrt(2)}` I get the following error statistics:

```
max_rel_error = 8.34405e-07
rms_rel_error = 2.76654e-07
```

If I widen the range to all normal float I see lower accuracy for arguments where the result is subnormal, e.g. for `y = sqrt(2)`:

```
max_rel_error = 0.666667
rms = 6.8727e-05
count = 1335165689
argmax = 2.56049e-32, 2.10195e-45 != 1.4013e-45
```

which seems reasonable, since these results are subnormals with only couple of significant bits left.
This commit is contained in:
Rasmus Munk Larsen
2021-01-18 13:25:16 +00:00
committed by David Tellenbach
parent bde6741641
commit cdd8fdc32e
5 changed files with 270 additions and 9 deletions
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38
Eigen/src/Core/arch/SSE/PacketMath.h
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@@ -26,7 +26,7 @@ namespace internal {
#ifdef EIGEN_VECTORIZE_FMA
#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD 1
#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
#endif
#endif
@@ -147,13 +147,13 @@ struct packet_traits<float> : default_packet_traits {
HasTanh = EIGEN_FAST_MATH,
HasErf = EIGEN_FAST_MATH,
HasBlend = 1,
HasCeil = 1,
HasFloor = 1
#ifdef EIGEN_VECTORIZE_SSE4_1
,
HasRint = 1,
HasRound = 1,
HasCeil = 1
HasRound = 1
#endif
};
};
@@ -173,14 +173,14 @@ struct packet_traits<double> : default_packet_traits {
HasExp = 1,
HasSqrt = 1,
HasRsqrt = 1,
HasBlend = 1
HasBlend = 1,
HasFloor = 1,
HasCeil = 1
#ifdef EIGEN_VECTORIZE_SSE4_1
,
HasRound = 1,
HasRint = 1,
HasFloor = 1,
HasCeil = 1
HasRint = 1
#endif
};
};
@@ -650,6 +650,30 @@ template<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a)
mask = pand(mask, cst_1);
return psub(tmp, mask);
}
template<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a)
{
const Packet4f cst_1 = pset1<Packet4f>(1.0f);
Packet4i emm0 = _mm_cvttps_epi32(a);
Packet4f tmp = _mm_cvtepi32_ps(emm0);
/* if greater, substract 1 */
Packet4f mask = _mm_cmplt_ps(tmp, a);
mask = pand(mask, cst_1);
return padd(tmp, mask);
}
// WARNING: this pfloor implementation makes sense for small inputs only,
// It is currently only used by pexp and not exposed through HasFloor.
template<> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a)
{
const Packet2d cst_1 = pset1<Packet2d>(1.0);
Packet4i emm0 = _mm_cvttpd_epi32(a);
Packet2d tmp = _mm_cvtepi32_pd(emm0);
/* if greater, substract 1 */
Packet2d mask = _mm_cmplt_pd(tmp, a);
mask = pand(mask, cst_1);
return padd(tmp, mask);
}
#endif
template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_ps(from); }