xref: /llvm-project/libc/src/math/generic/cospif16.cpp (revision 6a865b6d3d44e53adc9342fb2d80a604f5459707)

//===-- Half-precision cospif 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/cospif16.h"
#include "hdr/errno_macros.h"
#include "hdr/fenv_macros.h"
#include "sincosf16_utils.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/cast.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/macros/optimization.h"

namespace LIBC_NAMESPACE_DECL {

LLVM_LIBC_FUNCTION(float16, cospif16, (float16 x)) {
  using FPBits = typename fputil::FPBits<float16>;
  FPBits xbits(x);

  uint16_t x_u = xbits.uintval();
  uint16_t x_abs = x_u & 0x7fff;
  float xf = x;

  // 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 cosine of sum
  // formula:
  //   cos(x * pi) = cos((k + y) * pi/32)
  //               = cos(k * pi/32) * cos(y * pi/32) +
  //                 sin(y * pi/32) * sin(k * pi/32)

  // For signed zeros
  if (LIBC_UNLIKELY(x_abs == 0U))
    return fputil::cast<float16>(1.0f);

  // Numbers greater or equal to 2^10 are integers, or infinity, or NaN
  if (LIBC_UNLIKELY(x_abs >= 0x6400)) {
    if (LIBC_UNLIKELY(x_abs <= 0x67FF))
      return fputil::cast<float16>((x_abs & 0x1) ? -1.0f : 1.0f);

    // Check for NaN or infintiy values
    if (LIBC_UNLIKELY(x_abs >= 0x7c00)) {
      // If value is equal to infinity
      if (x_abs == 0x7c00) {
        fputil::set_errno_if_required(EDOM);
        fputil::raise_except_if_required(FE_INVALID);
      }

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

    return fputil::cast<float16>(1.0f);
  }

  float sin_k, cos_k, sin_y, cosm1_y;
  sincospif16_eval(xf, sin_k, cos_k, sin_y, cosm1_y);

  if (LIBC_UNLIKELY(sin_y == 0 && cos_k == 0))
    return fputil::cast<float16>(0.0f);

  // Since, cosm1_y = cos_y - 1, therefore:
  //   cos(x * pi) = cos_k(cosm1_y) + cos_k - sin_k * sin_y
  return fputil::cast<float16>(fputil::multiply_add(
      cos_k, cosm1_y, fputil::multiply_add(-sin_k, sin_y, cos_k)));
}

} // namespace LIBC_NAMESPACE_DECL