libc/src/math/generic/inv_trigf_utils.h

//===-- Single-precision general inverse trigonometric functions ----------===//
//
// 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_MATH_GENERIC_INV_TRIGF_UTILS_H
#define LLVM_LIBC_SRC_MATH_GENERIC_INV_TRIGF_UTILS_H

#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/common.h"

namespace LIBC_NAMESPACE {

// PI and PI / 2
constexpr double M_MATH_PI = 0x1.921fb54442d18p+1;
constexpr double M_MATH_PI_2 = 0x1.921fb54442d18p+0;

extern double ATAN_COEFFS[17][9];

// For |x| <= 1/32 and 0 <= i <= 16, return Q(x) such that:
//   Q(x) ~ (atan(x + i/16) - atan(i/16)) / x.
LIBC_INLINE double atan_eval(double x, int i) {
  double x2 = x * x;

  double c0 = fputil::multiply_add(x, ATAN_COEFFS[i][2], ATAN_COEFFS[i][1]);
  double c1 = fputil::multiply_add(x, ATAN_COEFFS[i][4], ATAN_COEFFS[i][3]);
  double c2 = fputil::multiply_add(x, ATAN_COEFFS[i][6], ATAN_COEFFS[i][5]);
  double c3 = fputil::multiply_add(x, ATAN_COEFFS[i][8], ATAN_COEFFS[i][7]);

  double x4 = x2 * x2;
  double d1 = fputil::multiply_add(x2, c1, c0);
  double d2 = fputil::multiply_add(x2, c3, c2);
  double p = fputil::multiply_add(x4, d2, d1);
  return p;
}

// > Q = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20|],
//                 [|1, D...|], [0, 0.5]);
constexpr double ASIN_COEFFS[10] = {0x1.5555555540fa1p-3, 0x1.333333512edc2p-4,
                                    0x1.6db6cc1541b31p-5, 0x1.f1caff324770ep-6,
                                    0x1.6e43899f5f4f4p-6, 0x1.1f847cf652577p-6,
                                    0x1.9b60f47f87146p-7, 0x1.259e2634c494fp-6,
                                    -0x1.df946fa875ddp-8, 0x1.02311ecf99c28p-5};

// Evaluate P(x^2) - 1, where P(x^2) ~ asin(x)/x
LIBC_INLINE double asin_eval(double xsq) {
  double x4 = xsq * xsq;
  double r1 = fputil::polyeval(x4, ASIN_COEFFS[0], ASIN_COEFFS[2],
                               ASIN_COEFFS[4], ASIN_COEFFS[6], ASIN_COEFFS[8]);
  double r2 = fputil::polyeval(x4, ASIN_COEFFS[1], ASIN_COEFFS[3],
                               ASIN_COEFFS[5], ASIN_COEFFS[7], ASIN_COEFFS[9]);
  return fputil::multiply_add(xsq, r2, r1);
}

} // namespace LIBC_NAMESPACE

#endif // LLVM_LIBC_SRC_MATH_GENERIC_INV_TRIGF_UTILS_H