libc/src/math/generic/tanpif.cpp

//===-- Single-precision tanpi function -----------------------------------===//
//
// 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
//
//===----------------------------------------------------------------------===//

#include "src/math/tanpif.h"
#include "sincosf_utils.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/cast.h"
#include "src/__support/FPUtil/except_value_utils.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/common.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY

namespace LIBC_NAMESPACE_DECL {

#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
constexpr size_t N_EXCEPTS = 3;

constexpr fputil::ExceptValues<float, N_EXCEPTS> TANPIF_EXCEPTS{{
    // (input, RZ output, RU offset, RD offset, RN offset)
    {0x38F26685, 0x39BE6182, 1, 0, 0},
    {0x3E933802, 0x3FA267DD, 1, 0, 0},
    {0x3F3663FF, 0xBFA267DD, 0, 1, 0},
}};
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS

LLVM_LIBC_FUNCTION(float, tanpif, (float x)) {
  using FPBits = typename fputil::FPBits<float>;
  FPBits xbits(x);

  uint32_t x_u = xbits.uintval();
  uint32_t x_abs = x_u & 0x7fff'ffffU;
  double xd = static_cast<double>(xbits.get_val());

  // Handle exceptional values
  if (LIBC_UNLIKELY(x_abs <= 0x3F3663FF)) {
    if (LIBC_UNLIKELY(x_abs == 0U))
      return x;

#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
    bool x_sign = x_u >> 31;

    if (auto r = TANPIF_EXCEPTS.lookup_odd(x_abs, x_sign);
        LIBC_UNLIKELY(r.has_value()))
      return r.value();
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
  }

  // Numbers greater or equal to 2^23 are always integers, or infinity, or NaN
  if (LIBC_UNLIKELY(x_abs >= 0x4B00'0000)) {
    // x is inf or NaN.
    if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) {
      if (xbits.is_signaling_nan()) {
        fputil::raise_except_if_required(FE_INVALID);
        return FPBits::quiet_nan().get_val();
      }

      if (x_abs == 0x7f80'0000U) {
        fputil::set_errno_if_required(EDOM);
        fputil::raise_except_if_required(FE_INVALID);
      }

      return x + FPBits::quiet_nan().get_val();
    }

    return FPBits::zero(xbits.sign()).get_val();
  }

  // Range reduction:
  // For |x| > 1/32, we perform range reduction as follows:
  // Find k and y such that:
  //   x = (k + y) * 1/32
  //   k is an integer
  //   |y| < 0.5
  //
  // This is done by performing:
  //   k = round(x * 32)
  //   y = x * 32 - k
  //
  // Once k and y are computed, we then deduce the answer by the formula:
  // tan(x) = sin(x) / cos(x)
  //        = (sin_y * cos_k + cos_y * sin_k) / (cos_y * cos_k - sin_y * sin_k)
  double sin_k, cos_k, sin_y, cosm1_y;
  sincospif_eval(xd, sin_k, cos_k, sin_y, cosm1_y);

  if (LIBC_UNLIKELY(sin_y == 0 && cos_k == 0)) {
    fputil::set_errno_if_required(EDOM);
    fputil::raise_except_if_required(FE_DIVBYZERO);

    int32_t x_mp5_i = static_cast<int32_t>(xd - 0.5);
    return FPBits::inf((x_mp5_i & 0x1) ? Sign::NEG : Sign::POS).get_val();
  }

  using fputil::multiply_add;
  return fputil::cast<float>(
      multiply_add(sin_y, cos_k, multiply_add(cosm1_y, sin_k, sin_k)) /
      multiply_add(sin_y, -sin_k, multiply_add(cosm1_y, cos_k, cos_k)));
}

} // namespace LIBC_NAMESPACE_DECL