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Improve accuracy of fast approximate tanh and the logistic functions in Eigen, such that they preserve relative accuracy to within a few ULPs where their function values tend to zero (around x=0 for tanh, and for large negative x for the logistic function).

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This change re-instates the fast rational approximation of the logistic function for float32 in Eigen (removed in 66f07efeae), but uses the more accurate approximation 1/(1+exp(-1)) ~= exp(x) below -9. The exponential is only calculated on the vectorized path if at least one element in the SIMD input vector is less than -9.

This change also contains a few improvements to speed up the original float specialization of logistic:
  - Introduce EIGEN_PREDICT_{FALSE,TRUE} for __builtin_predict and use it to predict that the logistic-only path is most likely (~2-3% speedup for the common case).
  - Carefully set the upper clipping point to the smallest x where the approximation evaluates to exactly 1. This saves the explicit clamping of the output (~7% speedup).

The increased accuracy for tanh comes at a cost of 10-20% depending on instruction set.

The benchmarks below repeated calls

   u = v.logistic()  (u = v.tanh(), respectively)

where u and v are of type Eigen::ArrayXf, have length 8k, and v contains random numbers in [-1,1].

Benchmark numbers for logistic:

Before:
Benchmark                  Time(ns)        CPU(ns)     Iterations
-----------------------------------------------------------------
SSE
BM_eigen_logistic_float        4467           4468         155835  model_time: 4827
AVX
BM_eigen_logistic_float        2347           2347         299135  model_time: 2926
AVX+FMA
BM_eigen_logistic_float        1467           1467         476143  model_time: 2926
AVX512
BM_eigen_logistic_float         805            805         858696  model_time: 1463

After:
Benchmark                  Time(ns)        CPU(ns)     Iterations
-----------------------------------------------------------------
SSE
BM_eigen_logistic_float        2589           2590         270264  model_time: 4827
AVX
BM_eigen_logistic_float        1428           1428         489265  model_time: 2926
AVX+FMA
BM_eigen_logistic_float        1059           1059         662255  model_time: 2926
AVX512
BM_eigen_logistic_float         673            673        1000000  model_time: 1463

Benchmark numbers for tanh:

Before:
Benchmark                  Time(ns)        CPU(ns)     Iterations
-----------------------------------------------------------------
SSE
BM_eigen_tanh_float        2391           2391         292624  model_time: 4242
AVX
BM_eigen_tanh_float        1256           1256         554662  model_time: 2633
AVX+FMA
BM_eigen_tanh_float         823            823         866267  model_time: 1609
AVX512
BM_eigen_tanh_float         443            443        1578999  model_time: 805

After:
Benchmark                  Time(ns)        CPU(ns)     Iterations
-----------------------------------------------------------------
SSE
BM_eigen_tanh_float        2588           2588         273531  model_time: 4242
AVX
BM_eigen_tanh_float        1536           1536         452321  model_time: 2633
AVX+FMA
BM_eigen_tanh_float        1007           1007         694681  model_time: 1609
AVX512
BM_eigen_tanh_float         471            471        1472178  model_time: 805
This commit is contained in:
Rasmus Munk Larsen
2019-12-16 21:33:42 +00:00
parent 8e5da71466
commit a566074480
9 changed files with 191 additions and 23 deletions
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10
Eigen/src/Core/arch/AVX/PacketMath.h
View File

@@ -297,9 +297,14 @@ template<> EIGEN_STRONG_INLINE Packet4d pmax<Packet4d>(const Packet4d& a, const
template<> EIGEN_STRONG_INLINE Packet8f pcmp_le(const Packet8f& a, const Packet8f& b) { return _mm256_cmp_ps(a,b,_CMP_LE_OQ); }
template<> EIGEN_STRONG_INLINE Packet8f pcmp_lt(const Packet8f& a, const Packet8f& b) { return _mm256_cmp_ps(a,b,_CMP_LT_OQ); }
template<> EIGEN_STRONG_INLINE Packet8f pcmp_eq(const Packet8f& a, const Packet8f& b) { return _mm256_cmp_ps(a,b,_CMP_EQ_OQ); }
template<> EIGEN_STRONG_INLINE Packet4d pcmp_eq(const Packet4d& a, const Packet4d& b) { return _mm256_cmp_pd(a,b,_CMP_EQ_OQ); }
template<> EIGEN_STRONG_INLINE Packet8f pcmp_lt_or_nan(const Packet8f& a, const Packet8f& b) { return _mm256_cmp_ps(a, b, _CMP_NGE_UQ); }
template<> EIGEN_STRONG_INLINE Packet8f pcmp_eq(const Packet8f& a, const Packet8f& b) { return _mm256_cmp_ps(a,b,_CMP_EQ_OQ); }
template<> EIGEN_STRONG_INLINE Packet4d pcmp_le(const Packet4d& a, const Packet4d& b) { return _mm256_cmp_pd(a,b,_CMP_LE_OQ); }
template<> EIGEN_STRONG_INLINE Packet4d pcmp_lt(const Packet4d& a, const Packet4d& b) { return _mm256_cmp_pd(a,b,_CMP_LT_OQ); }
template<> EIGEN_STRONG_INLINE Packet4d pcmp_lt_or_nan(const Packet4d& a, const Packet4d& b) { return _mm256_cmp_pd(a, b, _CMP_NGE_UQ); }
template<> EIGEN_STRONG_INLINE Packet4d pcmp_eq(const Packet4d& a, const Packet4d& b) { return _mm256_cmp_pd(a,b,_CMP_EQ_OQ); }
template<> EIGEN_STRONG_INLINE Packet8i pcmp_eq(const Packet8i& a, const Packet8i& b) {
#ifdef EIGEN_VECTORIZE_AVX2
@@ -311,6 +316,7 @@ template<> EIGEN_STRONG_INLINE Packet8i pcmp_eq(const Packet8i& a, const Packet8
#endif
}
template<> EIGEN_STRONG_INLINE Packet8f pceil<Packet8f>(const Packet8f& a) { return _mm256_ceil_ps(a); }
template<> EIGEN_STRONG_INLINE Packet4d pceil<Packet4d>(const Packet4d& a) { return _mm256_ceil_pd(a); }

30
Eigen/src/Core/arch/AVX512/PacketMath.h
View File

@@ -365,6 +365,12 @@ EIGEN_STRONG_INLINE Packet16f cat256(Packet8f a, Packet8f b) {
}
#endif
template <>
EIGEN_STRONG_INLINE Packet16f pcmp_eq(const Packet16f& a, const Packet16f& b) {
__mmask16 mask = _mm512_cmp_ps_mask(a, b, _CMP_EQ_OQ);
return _mm512_castsi512_ps(
_mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu));
}
template<> EIGEN_STRONG_INLINE Packet16f pcmp_le(const Packet16f& a, const Packet16f& b) {
__mmask16 mask = _mm512_cmp_ps_mask(a, b, _CMP_LE_OQ);
return _mm512_castsi512_ps(
@@ -388,12 +394,6 @@ template<> EIGEN_STRONG_INLINE Packet16i pcmp_eq(const Packet16i& a, const Packe
return _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu);
}
template <>
EIGEN_STRONG_INLINE Packet16f pcmp_eq(const Packet16f& a, const Packet16f& b) {
__mmask16 mask = _mm512_cmp_ps_mask(a, b, _CMP_EQ_OQ);
return _mm512_castsi512_ps(
_mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu));
}
template <>
EIGEN_STRONG_INLINE Packet8d pcmp_eq(const Packet8d& a, const Packet8d& b) {
@@ -401,6 +401,24 @@ EIGEN_STRONG_INLINE Packet8d pcmp_eq(const Packet8d& a, const Packet8d& b) {
return _mm512_castsi512_pd(
_mm512_mask_set1_epi64(_mm512_set1_epi64(0), mask, 0xffffffffffffffffu));
}
template <>
EIGEN_STRONG_INLINE Packet8d pcmp_le(const Packet8d& a, const Packet8d& b) {
__mmask8 mask = _mm512_cmp_pd_mask(a, b, _CMP_LE_OQ);
return _mm512_castsi512_pd(
_mm512_mask_set1_epi64(_mm512_set1_epi64(0), mask, 0xffffffffffffffffu));
}
template <>
EIGEN_STRONG_INLINE Packet8d pcmp_lt(const Packet8d& a, const Packet8d& b) {
__mmask8 mask = _mm512_cmp_pd_mask(a, b, _CMP_LT_OQ);
return _mm512_castsi512_pd(
_mm512_mask_set1_epi64(_mm512_set1_epi64(0), mask, 0xffffffffffffffffu));
}
template <>
EIGEN_STRONG_INLINE Packet8d pcmp_lt_or_nan(const Packet8d& a, const Packet8d& b) {
__mmask8 mask = _mm512_cmp_pd_mask(a, b, _CMP_NGT_UQ);
return _mm512_castsi512_pd(
_mm512_mask_set1_epi64(_mm512_set1_epi64(0), mask, 0xffffffffffffffffu));
}
template <>
EIGEN_STRONG_INLINE Packet16i ptrue<Packet16i>(const Packet16i& /*a*/) {

34
Eigen/src/Core/arch/GPU/PacketMath.h
View File

@@ -156,6 +156,15 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double eq_mask(const double& a,
return __longlong_as_double(a == b ? 0xffffffffffffffffull : 0ull);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float lt_mask(const float& a,
const float& b) {
return __int_as_float(a < b ? 0xffffffffu : 0u);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double lt_mask(const double& a,
const double& b) {
return __longlong_as_double(a < b ? 0xffffffffffffffffull : 0ull);
}
} // namespace
template <>
@@ -213,10 +222,21 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pcmp_eq<float4>(const float4& a,
eq_mask(a.w, b.w));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pcmp_lt<float4>(const float4& a,
const float4& b) {
return make_float4(lt_mask(a.x, b.x), lt_mask(a.y, b.y), lt_mask(a.z, b.z),
lt_mask(a.w, b.w));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
pcmp_eq<double2>(const double2& a, const double2& b) {
return make_double2(eq_mask(a.x, b.x), eq_mask(a.y, b.y));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
pcmp_lt<double2>(const double2& a, const double2& b) {
return make_double2(lt_mask(a.x, b.x), lt_mask(a.y, b.y));
}
#endif // EIGEN_CUDA_ARCH || defined(EIGEN_HIP_DEVICE_COMPILE)
template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 plset<float4>(const float& a) {
@@ -646,6 +666,20 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcmp_eq<half2>(const half2& a,
return __halves2half2(eq1, eq2);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcmp_lt<half2>(const half2& a,
const half2& b) {
half true_half = half_impl::raw_uint16_to_half(0xffffu);
half false_half = half_impl::raw_uint16_to_half(0x0000u);
half a1 = __low2half(a);
half a2 = __high2half(a);
half b1 = __low2half(b);
half b2 = __high2half(b);
half eq1 = __half2float(a1) < __half2float(b1) ? true_half : false_half;
half eq2 = __half2float(a2) < __half2float(b2) ? true_half : false_half;
return __halves2half2(eq1, eq2);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pand<half2>(const half2& a,
const half2& b) {

2
Eigen/src/Core/arch/NEON/PacketMath.h
View File

@@ -713,6 +713,8 @@ template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, con
return vreinterpretq_f64_u64(vbicq_u64(vreinterpretq_u64_f64(a),vreinterpretq_u64_f64(b)));
}
template<> EIGEN_STRONG_INLINE Packet2d pcmp_le(const Packet2d& a, const Packet2d& b) { return vreinterpretq_f64_u64(vcleq_f64(a,b)); }
template<> EIGEN_STRONG_INLINE Packet2d pcmp_lt(const Packet2d& a, const Packet2d& b) { return vreinterpretq_f64_u64(vcltq_f64(a,b)); }
template<> EIGEN_STRONG_INLINE Packet2d pcmp_eq(const Packet2d& a, const Packet2d& b) { return vreinterpretq_f64_u64(vceqq_f64(a,b)); }
template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from) { EIGEN_DEBUG_ALIGNED_LOAD return vld1q_f64(from); }

13
Eigen/src/Core/arch/SSE/PacketMath.h
View File

@@ -384,10 +384,17 @@ template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const
template<> EIGEN_STRONG_INLINE Packet4f pcmp_le(const Packet4f& a, const Packet4f& b) { return _mm_cmple_ps(a,b); }
template<> EIGEN_STRONG_INLINE Packet4f pcmp_lt(const Packet4f& a, const Packet4f& b) { return _mm_cmplt_ps(a,b); }
template<> EIGEN_STRONG_INLINE Packet4f pcmp_eq(const Packet4f& a, const Packet4f& b) { return _mm_cmpeq_ps(a,b); }
template<> EIGEN_STRONG_INLINE Packet4i pcmp_eq(const Packet4i& a, const Packet4i& b) { return _mm_cmpeq_epi32(a,b); }
template<> EIGEN_STRONG_INLINE Packet2d pcmp_eq(const Packet2d& a, const Packet2d& b) { return _mm_cmpeq_pd(a,b); }
template<> EIGEN_STRONG_INLINE Packet4f pcmp_lt_or_nan(const Packet4f& a, const Packet4f& b) { return _mm_cmpnge_ps(a,b); }
template<> EIGEN_STRONG_INLINE Packet4f pcmp_eq(const Packet4f& a, const Packet4f& b) { return _mm_cmpeq_ps(a,b); }
template<> EIGEN_STRONG_INLINE Packet2d pcmp_le(const Packet2d& a, const Packet2d& b) { return _mm_cmple_pd(a,b); }
template<> EIGEN_STRONG_INLINE Packet2d pcmp_lt(const Packet2d& a, const Packet2d& b) { return _mm_cmplt_pd(a,b); }
template<> EIGEN_STRONG_INLINE Packet2d pcmp_lt_or_nan(const Packet2d& a, const Packet2d& b) { return _mm_cmpnge_pd(a,b); }
template<> EIGEN_STRONG_INLINE Packet2d pcmp_eq(const Packet2d& a, const Packet2d& b) { return _mm_cmpeq_pd(a,b); }
template<> EIGEN_STRONG_INLINE Packet4i pcmp_lt(const Packet4i& a, const Packet4i& b) { return _mm_cmplt_epi32(a,b); }
template<> EIGEN_STRONG_INLINE Packet4i pcmp_eq(const Packet4i& a, const Packet4i& b) { return _mm_cmpeq_epi32(a,b); }
template<> EIGEN_STRONG_INLINE Packet4i ptrue<Packet4i>(const Packet4i& a) { return _mm_cmpeq_epi32(a, a); }
template<> EIGEN_STRONG_INLINE Packet4f