libc/src/math/generic/sinpif.cpp

//===-- Single-precision sinpif 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/sinpif.h"
#include "sincosf_utils.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/common.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY

namespace LIBC_NAMESPACE {

LLVM_LIBC_FUNCTION(float, sinpif, (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>(x);

  // Range reduction:
  // For |x| > pi/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
  // For small range (|x| < 2^45 when FMA instructions are available, 2^22
  // otherwise), 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 sine of sum
  // formula:
  //   sin(x * pi) = sin((k + y)*pi/32)
  //          = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
  // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..31 are precomputed
  // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
  // computed using degree-7 and degree-6 minimax polynomials generated by
  // Sollya respectively.

  // |x| <= 1/16
  if (LIBC_UNLIKELY(x_abs <= 0x3d80'0000U)) {

    if (LIBC_UNLIKELY(x_abs < 0x33CD'01D7U)) {
      if (LIBC_UNLIKELY(x_abs == 0U)) {
        // For signed zeros.
        return x;
      }

      // For very small values we can approximate sinpi(x) with x * pi
      // An exhaustive test shows that this is accurate for |x| < 9.546391 ×
      // 10-8
      double xdpi = xd * 0x1.921fb54442d18p1;
      return static_cast<float>(xdpi);
    }

    // |x| < 1/16.
    double xsq = xd * xd;

    // Degree-9 polynomial approximation:
    //   sinpi(x) ~ x + a_3 x^3 + a_5 x^5 + a_7 x^7 + a_9 x^9
    //          = x (1 + a_3 x^2 + ... + a_9 x^8)
    //          = x * P(x^2)
    // generated by Sollya with the following commands:
    // > display = hexadecimal;
    // > Q = fpminimax(sin(pi * x)/x, [|0, 2, 4, 6, 8|], [|D...|], [0, 1/16]);
    double result = fputil::polyeval(
        xsq, 0x1.921fb54442d18p1, -0x1.4abbce625bbf2p2, 0x1.466bc675e116ap1,
        -0x1.32d2c0b62d41cp-1, 0x1.501ec4497cb7dp-4);
    return static_cast<float>(xd * result);
  }

  // Numbers greater or equal to 2^23 are always integers or NaN
  if (LIBC_UNLIKELY(x_abs >= 0x4B00'0000)) {

    // check for NaN values
    if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) {
      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();
  }

  // Combine the results with the sine of sum formula:
  //   sin(x * pi) = sin((k + y)*pi/32)
  //          = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
  //          = sin_y * cos_k + (1 + cosm1_y) * sin_k
  //          = sin_y * cos_k + (cosm1_y * sin_k + 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 && sin_k == 0))
    return FPBits::zero(xbits.sign()).get_val();

  return static_cast<float>(fputil::multiply_add(
      sin_y, cos_k, fputil::multiply_add(cosm1_y, sin_k, sin_k)));
}

} // namespace LIBC_NAMESPACE