libc/src/math/generic/exp10f16.cpp

//===-- Half-precision 10^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/exp10f16.h"
#include "expxf16.h"
#include "hdr/errno_macros.h"
#include "hdr/fenv_macros.h"
#include "src/__support/CPP/array.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/except_value_utils.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/FPUtil/nearest_integer.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"
#include "src/__support/macros/properties/cpu_features.h"

namespace LIBC_NAMESPACE_DECL {

#ifdef LIBC_TARGET_CPU_HAS_FMA
static constexpr size_t N_EXP10F16_EXCEPTS = 5;
#else
static constexpr size_t N_EXP10F16_EXCEPTS = 8;
#endif

static constexpr fputil::ExceptValues<float16, N_EXP10F16_EXCEPTS>
    EXP10F16_EXCEPTS = {{
        // x = 0x1.8f4p-2, exp10f16(x) = 0x1.3ap+1 (RZ)
        {0x363dU, 0x40e8U, 1U, 0U, 1U},
        // x = 0x1.95cp-2, exp10f16(x) = 0x1.3ecp+1 (RZ)
        {0x3657U, 0x40fbU, 1U, 0U, 0U},
        // x = -0x1.018p-4, exp10f16(x) = 0x1.bbp-1 (RZ)
        {0xac06U, 0x3aecU, 1U, 0U, 0U},
        // x = -0x1.c28p+0, exp10f16(x) = 0x1.1ccp-6 (RZ)
        {0xbf0aU, 0x2473U, 1U, 0U, 0U},
        // x = -0x1.e1cp+1, exp10f16(x) = 0x1.694p-13 (RZ)
        {0xc387U, 0x09a5U, 1U, 0U, 0U},
#ifndef LIBC_TARGET_CPU_HAS_FMA
        // x = 0x1.0cp+1, exp10f16(x) = 0x1.f04p+6 (RZ)
        {0x4030U, 0x57c1U, 1U, 0U, 1U},
        // x = 0x1.1b8p+1, exp10f16(x) = 0x1.47cp+7 (RZ)
        {0x406eU, 0x591fU, 1U, 0U, 1U},
        // x = 0x1.1b8p+2, exp10f16(x) = 0x1.a4p+14 (RZ)
        {0x446eU, 0x7690U, 1U, 0U, 1U},
#endif
    }};

// Generated by Sollya with the following commands:
//   > display = hexadecimal;
//   > round(log2(10), SG, RN);
static constexpr float LOG2F_10 = 0x1.a934fp+1f;

// Generated by Sollya with the following commands:
//   > display = hexadecimal;
//   > round(log10(2), SG, RN);
static constexpr float LOG10F_2 = 0x1.344136p-2f;

LLVM_LIBC_FUNCTION(float16, exp10f16, (float16 x)) {
  using FPBits = fputil::FPBits<float16>;
  FPBits x_bits(x);

  uint16_t x_u = x_bits.uintval();
  uint16_t x_abs = x_u & 0x7fffU;

  // When |x| >= 5, or x is NaN.
  if (LIBC_UNLIKELY(x_abs >= 0x4500U)) {
    // exp10(NaN) = NaN
    if (x_bits.is_nan()) {
      if (x_bits.is_signaling_nan()) {
        fputil::raise_except_if_required(FE_INVALID);
        return FPBits::quiet_nan().get_val();
      }

      return x;
    }

    // When x >= 5.
    if (x_bits.is_pos()) {
      // exp10(+inf) = +inf
      if (x_bits.is_inf())
        return FPBits::inf().get_val();

      switch (fputil::quick_get_round()) {
      case FE_TONEAREST:
      case FE_UPWARD:
        fputil::set_errno_if_required(ERANGE);
        fputil::raise_except_if_required(FE_OVERFLOW);
        return FPBits::inf().get_val();
      default:
        return FPBits::max_normal().get_val();
      }
    }

    // When x <= -8.
    if (x_u >= 0xc800U) {
      // exp10(-inf) = +0
      if (x_bits.is_inf())
        return FPBits::zero().get_val();

      fputil::set_errno_if_required(ERANGE);
      fputil::raise_except_if_required(FE_UNDERFLOW | FE_INEXACT);

      if (fputil::fenv_is_round_up())
        return FPBits::min_subnormal().get_val();
      return FPBits::zero().get_val();
    }
  }

  // When x is 1, 2, 3, or 4. These are hard-to-round cases with exact results.
  if (LIBC_UNLIKELY((x_u & ~(0x3c00U | 0x4000U | 0x4200U | 0x4400U)) == 0)) {
    switch (x_u) {
    case 0x3c00U: // x = 1.0f16
      return static_cast<float16>(10.0);
    case 0x4000U: // x = 2.0f16
      return static_cast<float16>(100.0);
    case 0x4200U: // x = 3.0f16
      return static_cast<float16>(1'000.0);
    case 0x4400U: // x = 4.0f16
      return static_cast<float16>(10'000.0);
    }
  }

  if (auto r = EXP10F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
    return r.value();

  // For -8 < x < 5, to compute 10^x, we perform the following range reduction:
  // find hi, mid, lo, such that:
  //   x = (hi + mid) * log2(10) + lo, in which
  //     hi is an integer,
  //     mid * 2^3 is an integer,
  //     -2^(-4) <= lo < 2^(-4).
  // In particular,
  //   hi + mid = round(x * 2^3) * 2^(-3).
  // Then,
  //   10^x = 10^(hi + mid + lo) = 2^((hi + mid) * log2(10)) + 10^lo
  // We store 2^mid in the lookup table EXP2_MID_BITS, and compute 2^hi * 2^mid
  // by adding hi to the exponent field of 2^mid.  10^lo is computed using a
  // degree-4 minimax polynomial generated by Sollya.

  float xf = x;
  float kf = fputil::nearest_integer(xf * (LOG2F_10 * 0x1.0p+3f));
  int x_hi_mid = static_cast<int>(kf);
  int x_hi = x_hi_mid >> 3;
  int x_mid = x_hi_mid & 0x7;
  // lo = x - (hi + mid) = round(x * 2^3 * log2(10)) * log10(2) * (-2^(-3)) + x
  float lo = fputil::multiply_add(kf, LOG10F_2 * -0x1.0p-3f, xf);

  uint32_t exp2_hi_mid_bits =
      EXP2_MID_BITS[x_mid] +
      static_cast<uint32_t>(x_hi << fputil::FPBits<float>::FRACTION_LEN);
  float exp2_hi_mid = fputil::FPBits<float>(exp2_hi_mid_bits).get_val();
  // Degree-4 minimax polynomial generated by Sollya with the following
  // commands:
  //   > display = hexadecimal;
  //   > P = fpminimax((10^x - 1)/x, 3, [|SG...|], [-2^-4, 2^-4]);
  //   > 1 + x * P;
  float exp10_lo = fputil::polyeval(lo, 0x1p+0f, 0x1.26bb14p+1f, 0x1.53526p+1f,
                                    0x1.04b434p+1f, 0x1.2bcf9ep+0f);
  return static_cast<float16>(exp2_hi_mid * exp10_lo);
}

} // namespace LIBC_NAMESPACE_DECL