libc/src/__support/math/asinhf.h

//===-- Implementation header for asinf -------------------------*- 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_MATH_ASINHF_H
#define LLVM_LIBC_SRC___SUPPORT_MATH_ASINHF_H

#include "acoshf_utils.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/FPUtil/sqrt.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY

namespace LIBC_NAMESPACE_DECL {

namespace math {

LIBC_INLINE constexpr float asinhf(float x) {
  using namespace acoshf_internal;
  using FPBits_t = typename fputil::FPBits<float>;
  FPBits_t xbits(x);
  uint32_t x_u = xbits.uintval();
  uint32_t x_abs = xbits.abs().uintval();

  // |x| <= 2^-3
  if (LIBC_UNLIKELY(x_abs <= 0x3e00'0000U)) {
    // |x| <= 2^-26
    if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {
      return static_cast<float>(LIBC_UNLIKELY(x_abs == 0)
                                    ? x
                                    : (x - 0x1.5555555555555p-3 * x * x * x));
    }

    // Generated by Sollya with:
    // > P = fpminimax(asinh(x)/x, [|0, 2, 4, 6, 8, 10, 12|], [|1, D...|],
    //                             [0, 2^-3]);
    // > dirtyinfnorm((asinh(x) - x*P)/asinh(x), [0, 2^-3]);
    // 0x1.ee29e366e2913deff32ed8fa17f94bfe277a5babbp-62
    constexpr double COEFFS[] = {
        -0x1.555555555551ap-3, 0x1.333333330f782p-4,  -0x1.6db6dafa7f405p-5,
        0x1.f1c67120a7cf1p-6,  -0x1.6e4b0e52674d3p-6, 0x1.10450cf441118p-6,
    };

    double x_d = x;
    double x_sq = x_d * x_d;
    double c0 = fputil::multiply_add(x_sq, COEFFS[1], COEFFS[0]);
    double c1 = fputil::multiply_add(x_sq, COEFFS[3], COEFFS[2]);
    double c2 = fputil::multiply_add(x_sq, COEFFS[5], COEFFS[4]);
    double x_4 = x_sq * x_sq;
    double x_3 = x_d * x_sq;
    double p = fputil::polyeval(x_4, c0, c1, c2);
    return static_cast<float>(fputil::multiply_add(x_3, p, x_d));
  }

  constexpr double SIGN[2] = {1.0, -1.0};
  double x_sign = SIGN[x_u >> 31];
  double x_a = static_cast<double>(FPBits_t(x_abs).get_val());

#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
  // Helper functions to set results for exceptional cases.
  auto round_result_slightly_down = [x_sign](float r) -> float {
    return fputil::multiply_add(static_cast<float>(x_sign), r,
                                static_cast<float>(x_sign) * (-0x1.0p-24f));
  };
  auto round_result_slightly_up = [x_sign](float r) -> float {
    return fputil::multiply_add(static_cast<float>(x_sign), r,
                                static_cast<float>(x_sign) * 0x1.0p-24f);
  };

  if (LIBC_UNLIKELY(x_abs >= 0x4b80'0000U)) {
    // |x| >= 2^24
    // We can approximate asinh(x) = sign(x) * log(2 * |x|).
    if (LIBC_UNLIKELY(x_abs >= FPBits_t::inf().uintval())) {
      if (xbits.is_signaling_nan()) {
        fputil::raise_except_if_required(FE_INVALID);
        return FPBits_t::quiet_nan().get_val();
      }

      return x;
    }

    // Exceptional cases when x > 2^24.
    switch (x_abs) {
    case 0x4bdd65a5: // |x| = 0x1.bacb4ap24f
      return round_result_slightly_down(0x1.1e0696p4f);
    case 0x4c803f2c: // |x| = 0x1.007e58p26f
      return round_result_slightly_down(0x1.2b786cp4f);
    case 0x4f8ffb03: // |x| = 0x1.1ff606p32f
      return round_result_slightly_up(0x1.6fdd34p4f);
    case 0x5c569e88: // |x| = 0x1.ad3d1p57f
      return round_result_slightly_up(0x1.45c146p5f);
    case 0x5e68984e: // |x| = 0x1.d1309cp61f
      return round_result_slightly_up(0x1.5c9442p5f);
    case 0x62f7a05a: // |x| = 0x1.ef40b4p70f
      return round_result_slightly_up(0x1.8efc9ap5f);
    case 0x655890d3: // |x| = 0x1.b121a6p75f
      return round_result_slightly_down(0x1.a9a3f2p5f);
    case 0x65de7ca6: // |x| = 0x1.bcf94cp76f
      return round_result_slightly_up(0x1.af66cp5f);
    case 0x6eb1a8ec: // |x| = 0x1.6351d8p94f
      return round_result_slightly_down(0x1.08b512p6f);
    case 0x76be09de: // |x| = 0x1.7c13bcp110f
      return round_result_slightly_up(0x1.35569p6f);
    case 0x7997f30a: // |x| = 0x1.2fe614p116f
      return round_result_slightly_up(0x1.451436p6f);
#ifndef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
    case 0x7967ec37: // |x| = 0x1.cfd86ep115f
      return round_result_slightly_up(0x1.43ff6ep6f);
    case 0x58719e31: // |x| = 0x1.e33c62p49f
      return round_result_slightly_down(0x1.1a576cp5f);
    case 0x71699003: // |x| = 0x1.d32006p99f
      return round_result_slightly_up(0x1.17aa2p6f);
#endif // !LIBC_TARGET_CPU_HAS_FMA_DOUBLE
    }

    return static_cast<float>(x_sign * log_eval(2.0 * x_a));

  } else {
    // Exceptional cases when x < 2^24.
    if (LIBC_UNLIKELY(x_abs == 0x45abaf26)) {
      // |x| = 0x1.575e4cp12f
      return round_result_slightly_down(0x1.29becap3f);
    }
    if (LIBC_UNLIKELY(x_abs == 0x49d29048)) {
      // |x| = 0x1.a5209p20f
      return round_result_slightly_down(0x1.e1b92p3f);
    }
#ifndef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
    if (LIBC_UNLIKELY(x_abs == 0x45e19b90)) {
      // |x| = 0x1.c3372p12f
      return round_result_slightly_down(0x1.327c5cp3f);
    }
#endif // !LIBC_TARGET_CPU_HAS_FMA_DOUBLE
  }
#else
  if (LIBC_UNLIKELY(x_abs >= FPBits_t::inf().uintval())) {
    if (xbits.is_signaling_nan()) {
      fputil::raise_except_if_required(FE_INVALID);
      return FPBits_t::quiet_nan().get_val();
    }

    return x;
  }
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS

  // asinh(x) = log(x + sqrt(x^2 + 1))
  return static_cast<float>(
      x_sign * log_eval(x_a + fputil::sqrt<double>(
                                  fputil::multiply_add(x_a, x_a, 1.0))));
}

} // namespace math

} // namespace LIBC_NAMESPACE_DECL

#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ASINHF_H