src/math/generic/logf.cpp

//===-- Single-precision log(x) 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/logf.h"
#include "common_constants.h" // Lookup table for (1/f) and log(f)
#include "src/__support/FPUtil/BasicOperations.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FMA.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/common.h"

// This is an algorithm for log(x) in single precision which is correctly
// rounded for all rounding modes, based on the implementation of log(x) from
// the RLIBM project at:
// https://people.cs.rutgers.edu/~sn349/rlibm

// Step 1 - Range reduction:
//   For x = 2^m * 1.mant, log(x) = m * log(2) + log(1.m)
//   If x is denormal, we normalize it by multiplying x by 2^23 and subtracting
//   m by 23.

// Step 2 - Another range reduction:
//   To compute log(1.mant), let f be the highest 8 bits including the hidden
// bit, and d be the difference (1.mant - f), i.e. the remaining 16 bits of the
// mantissa. Then we have the following approximation formula:
//   log(1.mant) = log(f) + log(1.mant / f)
//               = log(f) + log(1 + d/f)
//               ~ log(f) + P(d/f)
// since d/f is sufficiently small.
//   log(f) and 1/f are then stored in two 2^7 = 128 entries look-up tables.

// Step 3 - Polynomial approximation:
//   To compute P(d/f), we use a single degree-5 polynomial in double precision
// which provides correct rounding for all but few exception values.
//   For more detail about how this polynomial is obtained, please refer to the
// paper:
//   Lim, J. and Nagarakatte, S., "One Polynomial Approximation to Produce
// Correctly Rounded Results of an Elementary Function for Multiple
// Representations and Rounding Modes", Proceedings of the 49th ACM SIGPLAN
// Symposium on Principles of Programming Languages (POPL-2022), Philadelphia,
// USA, January 16-22, 2022.
// https://people.cs.rutgers.edu/~sn349/papers/rlibmall-popl-2022.pdf

namespace __llvm_libc {

LLVM_LIBC_FUNCTION(float, logf, (float x)) {
  constexpr double LOG_2 = 0x1.62e42fefa39efp-1;
  using FPBits = typename fputil::FPBits<float>;
  FPBits xbits(x);

  switch (FPBits(x).uintval()) {
  case 0x41178febU: // x = 0x1.2f1fd6p+3f
    if (fputil::get_round() == FE_TONEAREST)
      return 0x1.1fcbcep+1f;
    break;
  case 0x4c5d65a5U: // x = 0x1.bacb4ap+25f
    if (fputil::get_round() == FE_TONEAREST)
      return 0x1.1e0696p+4f;
    break;
  case 0x65d890d3U: // x = 0x1.b121a6p+76f
    if (fputil::get_round() == FE_TONEAREST)
      return 0x1.a9a3f2p+5f;
    break;
  case 0x6f31a8ecU: // x = 0x1.6351d8p+95f
    if (fputil::get_round() == FE_TONEAREST)
      return 0x1.08b512p+6f;
    break;
  case 0x3f800001U: // x = 0x1.000002p+0f
    if (fputil::get_round() == FE_UPWARD)
      return 0x1p-23f;
    return 0x1.fffffep-24f;
  case 0x500ffb03U: // x = 0x1.1ff606p+33f
    if (fputil::get_round() != FE_UPWARD)
      return 0x1.6fdd34p+4f;
    break;
  case 0x7a17f30aU: // x = 0x1.2fe614p+117f
    if (fputil::get_round() != FE_UPWARD)
      return 0x1.451436p+6f;
    break;
  case 0x5cd69e88U: // x = 0x1.ad3d1p+58f
    if (fputil::get_round() != FE_UPWARD)
      return 0x1.45c146p+5f;
    break;
  }

  int m = 0;

  if (xbits.uintval() < FPBits::MIN_NORMAL ||
      xbits.uintval() > FPBits::MAX_NORMAL) {
    if (xbits.is_zero()) {
      return static_cast<float>(FPBits::neg_inf());
    }
    if (xbits.get_sign() && !xbits.is_nan()) {
      return FPBits::build_nan(1 << (fputil::MantissaWidth<float>::VALUE - 1));
    }
    if (xbits.is_inf_or_nan()) {
      return x;
    }
    // Normalize denormal inputs.
    xbits.set_val(xbits.get_val() * 0x1.0p23f);
    m = -23;
  }

  m += xbits.get_exponent();
  // Set bits to 1.m
  xbits.set_unbiased_exponent(0x7F);
  int f_index = xbits.get_mantissa() >> 16;

  FPBits f = xbits;
  f.bits &= ~0x0000'FFFF;

  double d = static_cast<float>(xbits) - static_cast<float>(f);
  d *= ONE_OVER_F[f_index];

  double extra_factor =
      fputil::multiply_add(static_cast<double>(m), LOG_2, LOG_F[f_index]);

  double r = __llvm_libc::fputil::polyeval(
      d, extra_factor, 0x1.fffffffffffacp-1, -0x1.fffffffef9cb2p-2,
      0x1.5555513bc679ap-2, -0x1.fff4805ea441p-3, 0x1.930180dbde91ap-3);

  return static_cast<float>(r);
}

} // namespace __llvm_libc