Eigen::internal::generic_reciprocal_newton_step< Packet, Steps > Struct Template Reference

#include <MathFunctionsImpl.h>

Static Public Member Functions
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet	run (const Packet &a, const Packet &approx_a_recip)

Detailed Description

template<typename Packet, int Steps>
struct Eigen::internal::generic_reciprocal_newton_step< Packet, Steps >

Fast reciprocal using Newton-Raphson's method.

Preconditions:

1. The starting guess provided in approx_a_recip must have 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 correct result.
2. If a is zero, approx_a_recip must be infinite with the same sign as a.
3. If a is infinite, approx_a_recip must be zero with the same sign as a.

If the preconditions are satisfied, which they are for for the _*_rcp_ps instructions on x86, the result has a maximum relative error of 2 ulps, and correctly handles reciprocals of zero, infinity, and NaN.

Member Function Documentation

run()

template<typename Packet , int Steps>

static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet Eigen::internal::generic_reciprocal_newton_step< Packet, Steps >::run ( const Packet &  a, const Packet &  approx_a_recip  )

inlinestatic

                                                                                                         {
    using Scalar = typename unpacket_traits<Packet>::type;
    const Packet two = pset1<Packet>(Scalar(2));
    // 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);
    const Packet tmp = pnmadd(a, x, two);
    // If tmp is NaN, it means that a is either +/-0 or +/-Inf.
    // In this case return the approximation directly.
    const Packet is_not_nan = pcmp_eq(tmp, tmp);
    return pselect(is_not_nan, pmul(x, tmp), x);
  }

References a, Eigen::internal::pcmp_eq(), Eigen::internal::pmul(), Eigen::internal::pnmadd(), Eigen::internal::pselect(), tmp, and plotDoE::x.

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The documentation for this struct was generated from the following file:

• MathFunctionsImpl.h