src/__support/mathvec/expf.h

//===-- Implementation header for SIMD expf ---------------------*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#ifndef LLVM_LIBC_SRC___SUPPORT_MATHVEC_EXPF_H
#define LLVM_LIBC_SRC___SUPPORT_MATHVEC_EXPF_H

#include "expf_utils.h"
#include "src/__support/CPP/simd.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/common.h"

namespace LIBC_NAMESPACE_DECL {

namespace mathvec {

template <size_t N>
LIBC_INLINE static cpp::simd<double, N> inline_exp(cpp::simd<double, N> x) {
  constexpr cpp::simd<double, N> shift = 0x1.800000000ffc0p+46;

  // inv_ln2 = round(1/log(2), D, RN);
  constexpr cpp::simd<double, N> inv_ln2 = 0x1.71547652b82fep+0;
  cpp::simd<double, N> z = shift + x * inv_ln2;
  cpp::simd<double, N> n = z - shift;

  // ln2_hi = round(log(2), D, RN);
  // ln2_lo = round(log(2) - ln2_hi, D, RN);
  constexpr cpp::simd<double, N> ln2_hi = 0x1.62e42fefa39efp-1;
  constexpr cpp::simd<double, N> ln2_lo = 0x1.abc9e3b39803fp-56;

  cpp::simd<double, N> r = x;
  r = r - n * ln2_hi;
  r = r - n * ln2_lo;

  // Coefficients of exp approximation, generated by Sollya with:
  // poly = 1 + x;
  // for i from 2 to 5 do {
  //   r = remez(exp(x)-poly(x), 5-i, [-log(2)/128;log(2)/128], x^i, 1e-10);
  //   c = coeff(roundcoefficients(r, [|D ...|]), 0);
  //   poly = poly + x^i*c;
  //   c;
  // };
  constexpr cpp::simd<double, N> c0 = 0x1.fffffffffdbcep-2;
  constexpr cpp::simd<double, N> c1 = 0x1.55555555543c2p-3;
  constexpr cpp::simd<double, N> c2 = 0x1.555573c64f2e3p-5;
  constexpr cpp::simd<double, N> c3 = 0x1.111126b4eff73p-7;

  /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5.  */
  cpp::simd<double, N> r2 = r * r;
  cpp::simd<double, N> p01 = c0 + r * c1;
  cpp::simd<double, N> p23 = c2 + r * c3;
  cpp::simd<double, N> p04 = p01 + r2 * p23;
  cpp::simd<double, N> y = r + p04 * r2;

  cpp::simd<uint64_t, N> u = cpp::bit_cast<cpp::simd<uint64_t, N>>(z);
  cpp::simd<double, N> s = exp_lookup(u);
  return s + s * y;
}

template <size_t N>
LIBC_INLINE cpp::simd<float, N> expf(cpp::simd<float, N> x) {
  using FPBits = typename fputil::FPBits<float>;

  cpp::simd<bool, N> is_inf = x >= 0x1.62e38p+9;
  cpp::simd<bool, N> is_zero = x <= -0x1.628c2ap+9;
  cpp::simd<bool, N> is_special = is_inf | is_zero;

  cpp::simd<float, N> special_res = is_inf ? FPBits::inf().get_val() : 0.0f;

  cpp::simd<double, N> x_d = cpp::simd_cast<double, float, N>(x);
  cpp::simd<double, N> y = inline_exp(x_d);
  cpp::simd<float, N> ret = cpp::simd_cast<float, double, N>(y);
  return is_special ? special_res : ret;
}

} // namespace mathvec

} // namespace LIBC_NAMESPACE_DECL

#endif // LLVM_LIBC_SRC___SUPPORT_MATHVEC_EXPF_H