xref: /llvm-project/libc/src/math/generic/sincos.cpp (revision 51e9430a0c767243411d4b81c284700f89719277)

//===-- Double-precision sincos 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/sincos.h"
#include "hdr/errno_macros.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/double_double.h"
#include "src/__support/FPUtil/dyadic_float.h"
#include "src/__support/FPUtil/except_value_utils.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/FPUtil/rounding_mode.h"
#include "src/__support/common.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h"            // LIBC_UNLIKELY
#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
#include "src/math/generic/range_reduction_double_common.h"
#include "src/math/generic/sincos_eval.h"

#ifdef LIBC_TARGET_CPU_HAS_FMA
#include "range_reduction_double_fma.h"
#else
#include "range_reduction_double_nofma.h"
#endif // LIBC_TARGET_CPU_HAS_FMA

namespace LIBC_NAMESPACE_DECL {

using DoubleDouble = fputil::DoubleDouble;
using Float128 = typename fputil::DyadicFloat<128>;

LLVM_LIBC_FUNCTION(void, sincos, (double x, double *sin_x, double *cos_x)) {
  using FPBits = typename fputil::FPBits<double>;
  FPBits xbits(x);

  uint16_t x_e = xbits.get_biased_exponent();

  DoubleDouble y;
  unsigned k;
  LargeRangeReduction range_reduction_large{};

  // |x| < 2^16
  if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT)) {
    // |x| < 2^-7
    if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 7)) {
      // |x| < 2^-27
      if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 27)) {
        // Signed zeros.
        if (LIBC_UNLIKELY(x == 0.0)) {
          *sin_x = x;
          *cos_x = 1.0;
          return;
        }

        // For |x| < 2^-27, max(|sin(x) - x|, |cos(x) - 1|) < ulp(x)/2.
#ifdef LIBC_TARGET_CPU_HAS_FMA
        *sin_x = fputil::multiply_add(x, -0x1.0p-54, x);
        *cos_x = fputil::multiply_add(x, -x, 1.0);
#else
        *cos_x = fputil::round_result_slightly_down(1.0);

        if (LIBC_UNLIKELY(x_e < 4)) {
          int rounding_mode = fputil::quick_get_round();
          if (rounding_mode == FE_TOWARDZERO ||
              (xbits.sign() == Sign::POS && rounding_mode == FE_DOWNWARD) ||
              (xbits.sign() == Sign::NEG && rounding_mode == FE_UPWARD))
            *sin_x = FPBits(xbits.uintval() - 1).get_val();
        }
        *sin_x = fputil::multiply_add(x, -0x1.0p-54, x);
#endif // LIBC_TARGET_CPU_HAS_FMA
        return;
      }
      // No range reduction needed.
      k = 0;
      y.lo = 0.0;
      y.hi = x;
    } else {
      // Small range reduction.
      k = range_reduction_small(x, y);
    }
  } else {
    // Inf or NaN
    if (LIBC_UNLIKELY(x_e > 2 * FPBits::EXP_BIAS)) {
      // sin(+-Inf) = NaN
      if (xbits.get_mantissa() == 0) {
        fputil::set_errno_if_required(EDOM);
        fputil::raise_except_if_required(FE_INVALID);
      }
      *sin_x = *cos_x = x + FPBits::quiet_nan().get_val();
      return;
    }

    // Large range reduction.
    k = range_reduction_large.fast(x, y);
  }

  DoubleDouble sin_y, cos_y;

  [[maybe_unused]] double err = generic::sincos_eval(y, sin_y, cos_y);

  // Look up sin(k * pi/128) and cos(k * pi/128)
#ifdef LIBC_MATH_HAS_SMALL_TABLES
  // Memory saving versions.  Use 65-entry table.
  auto get_idx_dd = [](unsigned kk) -> DoubleDouble {
    unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
    DoubleDouble ans = SIN_K_PI_OVER_128[idx];
    if (kk & 128) {
      ans.hi = -ans.hi;
      ans.lo = -ans.lo;
    }
    return ans;
  };
  DoubleDouble sin_k = get_idx_dd(k);
  DoubleDouble cos_k = get_idx_dd(k + 64);
#else
  // Fast look up version, but needs 256-entry table.
  // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
  DoubleDouble sin_k = SIN_K_PI_OVER_128[k & 255];
  DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 255];
#endif // LIBC_MATH_HAS_SMALL_TABLES

  DoubleDouble msin_k{-sin_k.lo, -sin_k.hi};

  // After range reduction, k = round(x * 128 / pi) and y = x - k * (pi / 128).
  // So k is an integer and -pi / 256 <= y <= pi / 256.
  // Then sin(x) = sin((k * pi/128 + y)
  //             = sin(y) * cos(k*pi/128) + cos(y) * sin(k*pi/128)
  DoubleDouble sin_k_cos_y = fputil::quick_mult(cos_y, sin_k);
  DoubleDouble cos_k_sin_y = fputil::quick_mult(sin_y, cos_k);
  //      cos(x) = cos((k * pi/128 + y)
  //             = cos(y) * cos(k*pi/128) - sin(y) * sin(k*pi/128)
  DoubleDouble cos_k_cos_y = fputil::quick_mult(cos_y, cos_k);
  DoubleDouble msin_k_sin_y = fputil::quick_mult(sin_y, msin_k);

  DoubleDouble sin_dd =
      fputil::exact_add<false>(sin_k_cos_y.hi, cos_k_sin_y.hi);
  DoubleDouble cos_dd =
      fputil::exact_add<false>(cos_k_cos_y.hi, msin_k_sin_y.hi);
  sin_dd.lo += sin_k_cos_y.lo + cos_k_sin_y.lo;
  cos_dd.lo += msin_k_sin_y.lo + cos_k_cos_y.lo;

#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
  *sin_x = sin_dd.hi + sin_dd.lo;
  *cos_x = cos_dd.hi + cos_dd.lo;
  return;
#else
  // Accurate test and pass for correctly rounded implementation.

  double sin_lp = sin_dd.lo + err;
  double sin_lm = sin_dd.lo - err;
  double cos_lp = cos_dd.lo + err;
  double cos_lm = cos_dd.lo - err;

  double sin_upper = sin_dd.hi + sin_lp;
  double sin_lower = sin_dd.hi + sin_lm;
  double cos_upper = cos_dd.hi + cos_lp;
  double cos_lower = cos_dd.hi + cos_lm;

  // Ziv's rounding test.
  if (LIBC_LIKELY(sin_upper == sin_lower && cos_upper == cos_lower)) {
    *sin_x = sin_upper;
    *cos_x = cos_upper;
    return;
  }

  Float128 u_f128, sin_u, cos_u;
  if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT))
    u_f128 = range_reduction_small_f128(x);
  else
    u_f128 = range_reduction_large.accurate();

  generic::sincos_eval(u_f128, sin_u, cos_u);

  auto get_sin_k = [](unsigned kk) -> Float128 {
    unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
    Float128 ans = SIN_K_PI_OVER_128_F128[idx];
    if (kk & 128)
      ans.sign = Sign::NEG;
    return ans;
  };

  // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
  Float128 sin_k_f128 = get_sin_k(k);
  Float128 cos_k_f128 = get_sin_k(k + 64);
  Float128 msin_k_f128 = get_sin_k(k + 128);

  // TODO: Add assertion if Ziv's accuracy tests fail in debug mode.
  // https://github.com/llvm/llvm-project/issues/96452.

  if (sin_upper == sin_lower)
    *sin_x = sin_upper;
  else
    // sin(x) = sin((k * pi/128 + u)
    //        = sin(u) * cos(k*pi/128) + cos(u) * sin(k*pi/128)
    *sin_x = static_cast<double>(
        fputil::quick_add(fputil::quick_mul(sin_k_f128, cos_u),
                          fputil::quick_mul(cos_k_f128, sin_u)));

  if (cos_upper == cos_lower)
    *cos_x = cos_upper;
  else
    // cos(x) = cos((k * pi/128 + u)
    //        = cos(u) * cos(k*pi/128) - sin(u) * sin(k*pi/128)
    *cos_x = static_cast<double>(
        fputil::quick_add(fputil::quick_mul(cos_k_f128, cos_u),
                          fputil::quick_mul(msin_k_f128, sin_u)));

#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
}

} // namespace LIBC_NAMESPACE_DECL