Function exp10_denorm

system/lib/llvm-libc/src/math/generic/exp10.cpp:183–229

When output is denormal.

// When output is denormal.
double exp10_denorm(double x) {
  // Range reduction.
  double tmp = fputil::multiply_add(x, LOG2_10, 0x1.8000'0000'4p21);
  int k = static_cast<int>(cpp::bit_cast<uint64_t>(tmp) >> 19);
  double kd = static_cast<double>(k);

  uint32_t idx1 = (k >> 6) & 0x3f;
  uint32_t idx2 = k & 0x3f;

  int hi = k >> 12;

  DoubleDouble exp_mid1{EXP2_MID1[idx1].mid, EXP2_MID1[idx1].hi};
  DoubleDouble exp_mid2{EXP2_MID2[idx2].mid, EXP2_MID2[idx2].hi};
  DoubleDouble exp_mid = fputil::quick_mult(exp_mid1, exp_mid2);

  // |dx| < 1.5 * 2^-15 + 2^-31 < 2^-14
  double lo_h = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact
  double dx = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_MID, lo_h);

  double mid_lo = dx * exp_mid.hi;

  // Approximate (10^dx - 1)/dx ~ 1 + a0*dx + a1*dx^2 + a2*dx^3 + a3*dx^4.
  double p = poly_approx_d(dx);

  double lo = fputil::multiply_add(p, mid_lo, exp_mid.lo);

#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
  return ziv_test_denorm</*SKIP_ZIV_TEST=*/true>(hi, exp_mid.hi, lo, ERR_D)
      .value();
#else
  if (auto r = ziv_test_denorm(hi, exp_mid.hi, lo, ERR_D);
      LIBC_LIKELY(r.has_value()))
    return r.value();

  // Use double-double
  DoubleDouble r_dd = exp10_double_double(x, kd, exp_mid);

  if (auto r = ziv_test_denorm(hi, r_dd.hi, r_dd.lo, ERR_DD);
      LIBC_LIKELY(r.has_value()))
    return r.value();

  // Use 128-bit precision
  Float128 r_f128 = exp10_f128(x, kd, idx1, idx2);

  return static_cast<double>(r_f128);
#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
}

// Check for exceptional cases when:
//  * log10(1 - 2^-54) < x < log10(1 + 2^-53)