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Add packetized versions of i0e and i1e special functions.
- In particular refactor the i0e and i1e code so scalar and vectorized path share code. - Move chebevl to GenericPacketMathFunctions. A brief benchmark with building Eigen with FMA, AVX and AVX2 flags Before: CPU: Intel Haswell with HyperThreading (6 cores) Benchmark Time(ns) CPU(ns) Iterations ----------------------------------------------------------------- BM_eigen_i0e_double/1 57.3 57.3 10000000 BM_eigen_i0e_double/8 398 398 1748554 BM_eigen_i0e_double/64 3184 3184 218961 BM_eigen_i0e_double/512 25579 25579 27330 BM_eigen_i0e_double/4k 205043 205042 3418 BM_eigen_i0e_double/32k 1646038 1646176 422 BM_eigen_i0e_double/256k 13180959 13182613 53 BM_eigen_i0e_double/1M 52684617 52706132 10 BM_eigen_i0e_float/1 28.4 28.4 24636711 BM_eigen_i0e_float/8 75.7 75.7 9207634 BM_eigen_i0e_float/64 512 512 1000000 BM_eigen_i0e_float/512 4194 4194 166359 BM_eigen_i0e_float/4k 32756 32761 21373 BM_eigen_i0e_float/32k 261133 261153 2678 BM_eigen_i0e_float/256k 2087938 2088231 333 BM_eigen_i0e_float/1M 8380409 8381234 84 BM_eigen_i1e_double/1 56.3 56.3 10000000 BM_eigen_i1e_double/8 397 397 1772376 BM_eigen_i1e_double/64 3114 3115 223881 BM_eigen_i1e_double/512 25358 25361 27761 BM_eigen_i1e_double/4k 203543 203593 3462 BM_eigen_i1e_double/32k 1613649 1613803 428 BM_eigen_i1e_double/256k 12910625 12910374 54 BM_eigen_i1e_double/1M 51723824 51723991 10 BM_eigen_i1e_float/1 28.3 28.3 24683049 BM_eigen_i1e_float/8 74.8 74.9 9366216 BM_eigen_i1e_float/64 505 505 1000000 BM_eigen_i1e_float/512 4068 4068 171690 BM_eigen_i1e_float/4k 31803 31806 21948 BM_eigen_i1e_float/32k 253637 253692 2763 BM_eigen_i1e_float/256k 2019711 2019918 346 BM_eigen_i1e_float/1M 8238681 8238713 86 After: CPU: Intel Haswell with HyperThreading (6 cores) Benchmark Time(ns) CPU(ns) Iterations ----------------------------------------------------------------- BM_eigen_i0e_double/1 15.8 15.8 44097476 BM_eigen_i0e_double/8 99.3 99.3 7014884 BM_eigen_i0e_double/64 777 777 886612 BM_eigen_i0e_double/512 6180 6181 100000 BM_eigen_i0e_double/4k 48136 48140 14678 BM_eigen_i0e_double/32k 385936 385943 1801 BM_eigen_i0e_double/256k 3293324 3293551 228 BM_eigen_i0e_double/1M 12423600 12424458 57 BM_eigen_i0e_float/1 16.3 16.3 43038042 BM_eigen_i0e_float/8 30.1 30.1 23456931 BM_eigen_i0e_float/64 169 169 4132875 BM_eigen_i0e_float/512 1338 1339 516860 BM_eigen_i0e_float/4k 10191 10191 68513 BM_eigen_i0e_float/32k 81338 81337 8531 BM_eigen_i0e_float/256k 651807 651984 1000 BM_eigen_i0e_float/1M 2633821 2634187 268 BM_eigen_i1e_double/1 16.2 16.2 42352499 BM_eigen_i1e_double/8 110 110 6316524 BM_eigen_i1e_double/64 822 822 851065 BM_eigen_i1e_double/512 6480 6481 100000 BM_eigen_i1e_double/4k 51843 51843 10000 BM_eigen_i1e_double/32k 414854 414852 1680 BM_eigen_i1e_double/256k 3320001 3320568 212 BM_eigen_i1e_double/1M 13442795 13442391 53 BM_eigen_i1e_float/1 17.6 17.6 41025735 BM_eigen_i1e_float/8 35.5 35.5 19597891 BM_eigen_i1e_float/64 240 240 2924237 BM_eigen_i1e_float/512 1424 1424 485953 BM_eigen_i1e_float/4k 10722 10723 65162 BM_eigen_i1e_float/32k 86286 86297 8048 BM_eigen_i1e_float/256k 691821 691868 1000 BM_eigen_i1e_float/1M 2777336 2777747 256 This shows anywhere from a 50% to 75% improvement on these operations. I've also benchmarked without any of these flags turned on, and got similar performance to before (if not better). Also tested packetmath.cpp + special_functions to ensure no regressions.
This commit is contained in:
Srinivas Vasudevan
@@ -73,6 +73,8 @@ template<> struct packet_traits<float> : default_packet_traits
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HasExpm1 = 1,
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HasExp = 1,
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HasNdtri = 1,
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HasI0e = 1,
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HasI1e = 1,
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HasSqrt = 1,
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HasRsqrt = 1,
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HasTanh = EIGEN_FAST_MATH,
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@@ -99,6 +99,8 @@ template<> struct packet_traits<float> : default_packet_traits
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HasExpm1 = 1,
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HasNdtri = 1,
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#endif
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HasI0e = 1,
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HasI1e = 1,
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HasExp = 1,
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HasSqrt = EIGEN_FAST_MATH,
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HasRsqrt = EIGEN_FAST_MATH,
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@@ -570,6 +570,97 @@ struct ppolevl<Packet, 0> {
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}
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};
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/* chbevl (modified for Eigen)
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*
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* Evaluate Chebyshev series
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*
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*
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*
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* SYNOPSIS:
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*
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* int N;
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* Scalar x, y, coef[N], chebevl();
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*
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* y = chbevl( x, coef, N );
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*
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*
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*
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* DESCRIPTION:
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*
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* Evaluates the series
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*
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* N-1
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* - '
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* y = > coef[i] T (x/2)
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* - i
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* i=0
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*
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* of Chebyshev polynomials Ti at argument x/2.
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*
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* Coefficients are stored in reverse order, i.e. the zero
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* order term is last in the array. Note N is the number of
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* coefficients, not the order.
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*
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* If coefficients are for the interval a to b, x must
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* have been transformed to x -> 2(2x - b - a)/(b-a) before
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* entering the routine. This maps x from (a, b) to (-1, 1),
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* over which the Chebyshev polynomials are defined.
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*
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* If the coefficients are for the inverted interval, in
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* which (a, b) is mapped to (1/b, 1/a), the transformation
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* required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity,
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* this becomes x -> 4a/x - 1.
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*
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*
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*
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* SPEED:
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*
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* Taking advantage of the recurrence properties of the
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* Chebyshev polynomials, the routine requires one more
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* addition per loop than evaluating a nested polynomial of
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* the same degree.
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*
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*/
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template <typename Packet, int N>
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struct generic_cheb_recurrence {
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EIGEN_DEVICE_FUNC
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static EIGEN_STRONG_INLINE Packet run(Packet x, const typename unpacket_traits<Packet>::type coef[]) {
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EIGEN_STATIC_ASSERT((N > 2), YOU_MADE_A_PROGRAMMING_MISTAKE);
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return pmadd(
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generic_cheb_recurrence<Packet, N - 1>::run(x, coef), x,
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psub(pset1<Packet>(coef[N - 1]), generic_cheb_recurrence<Packet, N -
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2>::run(x, coef)));
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}
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};
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template <typename Packet>
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struct generic_cheb_recurrence<Packet, 2> {
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EIGEN_DEVICE_FUNC
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static EIGEN_STRONG_INLINE Packet run(Packet x, const typename unpacket_traits<Packet>::type coef[]) {
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return pmadd(pset1<Packet>(coef[0]), x, pset1<Packet>(coef[1]));
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}
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};
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template <typename Packet>
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struct generic_cheb_recurrence<Packet, 1> {
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EIGEN_DEVICE_FUNC
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static EIGEN_STRONG_INLINE Packet run(Packet x, const typename unpacket_traits<Packet>::type coef[]) {
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EIGEN_UNUSED_VARIABLE(x);
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return pset1<Packet>(coef[0]);
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}
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};
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template <typename Packet, int N>
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struct pchebevl {
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EIGEN_DEVICE_FUNC
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static EIGEN_STRONG_INLINE Packet run(Packet x, const typename unpacket_traits<Packet>::type coef[]) {
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const Packet half = pset1<Packet>(0.5);
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return pmul(half, psub(
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generic_cheb_recurrence<Packet, N>::run(x, coef),
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generic_cheb_recurrence<Packet, N - 2>::run(x, coef)));
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}
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};
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} // end namespace internal
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} // end namespace Eigen
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@@ -114,7 +114,8 @@ template<> struct packet_traits<float> : default_packet_traits
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HasExpm1 = 1,
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HasNdtri = 1,
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HasExp = 1,
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HasNdtri = 1,
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HasI0e = 1,
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HasI1e = 1,
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HasSqrt = 1,
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HasRsqrt = 1,
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HasTanh = EIGEN_FAST_MATH,
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@@ -215,6 +215,8 @@ template<typename Scalar> struct scalar_digamma_op;
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template<typename Scalar> struct scalar_erf_op;
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template<typename Scalar> struct scalar_erfc_op;
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template<typename Scalar> struct scalar_ndtri_op;
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template<typename Scalar> struct scalar_i0e_op;
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template<typename Scalar> struct scalar_i1e_op;
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template<typename Scalar> struct scalar_igamma_op;
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template<typename Scalar> struct scalar_igammac_op;
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template<typename Scalar> struct scalar_zeta_op;
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