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Add reciprocal packet op and fast specializations for float with SSE, AVX, and AVX512.

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This commit is contained in:
Rasmus Munk Larsen
2022-01-21 23:49:18 +00:00
parent 4b0926f99b
commit ea2c02060c
14 changed files with 95 additions and 63 deletions
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29
Eigen/src/Core/MathFunctionsImpl.h
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@@ -17,6 +17,35 @@ namespace Eigen {
namespace internal {
/** \internal Fast reciprocal using Newton-Raphson's method.
We assume that the starting guess provided in approx_a_recip has at least
half the leading mantissa bits in the correct result, such that a single
Newton-Raphson step is sufficient to get within 1-2 ulps of the currect result.
*/
template <typename Packet, int Steps>
struct generic_reciprocal_newton_step {
static_assert(Steps > 0, "Steps must be at least 1.");
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Packet
run(const Packet& a, const Packet& approx_a_recip) {
using Scalar = typename unpacket_traits<Packet>::type;
const Packet two = pset1<Packet>(Scalar(2));
const Packet neg_a = pnegate(a);
// Refine the approximation using one Newton-Raphson step:
// x_{i} = x_{i-1} * (2 - a * x_{i-1})
const Packet x =
generic_reciprocal_newton_step<Packet,Steps - 1>::run(a, approx_a_recip);
return pmul(x, pmadd(neg_a, x, two));
}
};
template<typename Packet>
struct generic_reciprocal_newton_step<Packet, 0> {
EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Packet
run(const Packet& /*unused*/, const Packet& approx_a_recip) {
return approx_a_recip;
}
};
/** \internal \returns the hyperbolic tan of \a a (coeff-wise)
Doesn't do anything fancy, just a 13/6-degree rational interpolant which
is accurate up to a couple of ulps in the (approximate) range [-8, 8],