/src/libjxl/lib/jxl/base/rational_polynomial-inl.h

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// Copyright (c) the JPEG XL Project Authors. All rights reserved.
//
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

// Fast SIMD evaluation of rational polynomials for approximating functions.

#if defined(LIB_JXL_BASE_RATIONAL_POLYNOMIAL_INL_H_) == \
    defined(HWY_TARGET_TOGGLE)
#ifdef LIB_JXL_BASE_RATIONAL_POLYNOMIAL_INL_H_
#undef LIB_JXL_BASE_RATIONAL_POLYNOMIAL_INL_H_
#else
#define LIB_JXL_BASE_RATIONAL_POLYNOMIAL_INL_H_
#endif

#include <jxl/types.h>
#include <stddef.h>

#include <hwy/highway.h>
HWY_BEFORE_NAMESPACE();
namespace jxl {
namespace HWY_NAMESPACE {
namespace {

// These templates are not found via ADL.
using hwy::HWY_NAMESPACE::ApproximateReciprocal;
using hwy::HWY_NAMESPACE::Div;
using hwy::HWY_NAMESPACE::MulAdd;

// Primary template: default to actual division.
template <typename T, class V>
struct FastDivision {
  HWY_INLINE V operator()(const V n, const V d) const { return n / d; }
};
// Partial specialization for float vectors.
template <class V>
struct FastDivision<float, V> {
  // One Newton-Raphson iteration.
  static HWY_INLINE V ReciprocalNR(const V x) {
    const auto rcp = ApproximateReciprocal(x);
    const auto sum = Add(rcp, rcp);
    const auto x_rcp = Mul(x, rcp);
    return NegMulAdd(x_rcp, rcp, sum);
  }

  V operator()(const V n, const V d) const {
#if JXL_TRUE  // Faster on SKX
    return Div(n, d);
#else
    return n * ReciprocalNR(d);
#endif
  }
};

// Approximates smooth functions via rational polynomials (i.e. dividing two
// polynomials). Evaluates polynomials via Horner's scheme, which is faster than
// Clenshaw recurrence for Chebyshev polynomials. LoadDup128 allows us to
// specify constants (replicated 4x) independently of the lane count.
template <size_t NP, size_t NQ, class D, class V, typename T>
HWY_INLINE HWY_MAYBE_UNUSED V EvalRationalPolynomial(const D d, const V x,
                                                     const T (&p)[NP],
                                                     const T (&q)[NQ]) {
  constexpr size_t kDegP = NP / 4 - 1;
  constexpr size_t kDegQ = NQ / 4 - 1;
  auto yp = LoadDup128(d, &p[kDegP * 4]);
  auto yq = LoadDup128(d, &q[kDegQ * 4]);
  // We use pointer arithmetic to refer to &p[(kDegP - n) * 4] to avoid a
  // compiler warning that the index is out of bounds since we are already
  // checking that it is not out of bounds with (kDegP >= n) and the access
  // will be optimized away. Similarly with q and kDegQ.
  HWY_FENCE;
  if (kDegP >= 1) yp = MulAdd(yp, x, LoadDup128(d, p + ((kDegP - 1) * 4)));
  if (kDegQ >= 1) yq = MulAdd(yq, x, LoadDup128(d, q + ((kDegQ - 1) * 4)));
  HWY_FENCE;
  if (kDegP >= 2) yp = MulAdd(yp, x, LoadDup128(d, p + ((kDegP - 2) * 4)));
  if (kDegQ >= 2) yq = MulAdd(yq, x, LoadDup128(d, q + ((kDegQ - 2) * 4)));
  HWY_FENCE;
  if (kDegP >= 3) yp = MulAdd(yp, x, LoadDup128(d, p + ((kDegP - 3) * 4)));
  if (kDegQ >= 3) yq = MulAdd(yq, x, LoadDup128(d, q + ((kDegQ - 3) * 4)));
  HWY_FENCE;
  if (kDegP >= 4) yp = MulAdd(yp, x, LoadDup128(d, p + ((kDegP - 4) * 4)));
  if (kDegQ >= 4) yq = MulAdd(yq, x, LoadDup128(d, q + ((kDegQ - 4) * 4)));
  HWY_FENCE;
  if (kDegP >= 5) yp = MulAdd(yp, x, LoadDup128(d, p + ((kDegP - 5) * 4)));
  if (kDegQ >= 5) yq = MulAdd(yq, x, LoadDup128(d, q + ((kDegQ - 5) * 4)));
  HWY_FENCE;
  if (kDegP >= 6) yp = MulAdd(yp, x, LoadDup128(d, p + ((kDegP - 6) * 4)));
  if (kDegQ >= 6) yq = MulAdd(yq, x, LoadDup128(d, q + ((kDegQ - 6) * 4)));
  HWY_FENCE;
  if (kDegP >= 7) yp = MulAdd(yp, x, LoadDup128(d, p + ((kDegP - 7) * 4)));
  if (kDegQ >= 7) yq = MulAdd(yq, x, LoadDup128(d, q + ((kDegQ - 7) * 4)));

  static_assert(kDegP < 8, "Polynomial degree is too high");
  static_assert(kDegQ < 8, "Polynomial degree is too high");

  return FastDivision<T, V>()(yp, yq);
}

}  // namespace
// NOLINTNEXTLINE(google-readability-namespace-comments)
}  // namespace HWY_NAMESPACE
}  // namespace jxl
HWY_AFTER_NAMESPACE();
#endif  // LIB_JXL_BASE_RATIONAL_POLYNOMIAL_INL_H_

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Created: 2025-08-11 08:01