libc/src/math/generic/log1pf.cpp

   1 //===-- Single-precision log1p(x) function --------------------------------===//
   2 //
   3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
   4 // See https://llvm.org/LICENSE.txt for license information.
   5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
   6 //
   7 //===----------------------------------------------------------------------===//
   8
   9 #include "src/math/log1pf.h"
  10 #include "common_constants.h" // Lookup table for (1/f) and log(f)
  11 #include "src/__support/FPUtil/FEnvImpl.h"
  12 #include "src/__support/FPUtil/FMA.h"
  13 #include "src/__support/FPUtil/FPBits.h"
  14 #include "src/__support/FPUtil/PolyEval.h"
  15 #include "src/__support/FPUtil/except_value_utils.h"
  16 #include "src/__support/FPUtil/multiply_add.h"
  17 #include "src/__support/common.h"
  18 #include "src/__support/macros/config.h"
  19 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
  20 #include "src/__support/macros/properties/cpu_features.h"
  21
  22 // This is an algorithm for log10(x) in single precision which is
  23 // correctly rounded for all rounding modes.
  24 // - An exhaustive test show that when x >= 2^45, log1pf(x) == logf(x)
  25 // for all rounding modes.
  26 // - When 2^(-6) <= |x| < 2^45, the sum (double(x) + 1.0) is exact,
  27 // so we can adapt the correctly rounded algorithm of logf to compute
  28 // log(double(x) + 1.0) correctly.  For more information about the logf
  29 // algorithm, see `libc/src/math/generic/logf.cpp`.
  30 // - When |x| < 2^(-6), we use a degree-8 polynomial in double precision
  31 // generated with Sollya using the following command:
  32 //   fpminimax(log(1 + x)/x, 7, [|D...|], [-2^-6; 2^-6]);
  33
  34 namespace LIBC_NAMESPACE_DECL {
  35
  36 namespace internal {
  37
  38 // We don't need to treat denormal and 0
  39 LIBC_INLINE float log(double x) {
  40   constexpr double LOG_2 = 0x1.62e42fefa39efp-1;
  41
  42   using FPBits = typename fputil::FPBits<double>;
  43   FPBits xbits(x);
  44
  45   uint64_t x_u = xbits.uintval();
  46
  47   if (LIBC_UNLIKELY(x_u > FPBits::max_normal().uintval())) {
  48     if (xbits.is_neg() && !xbits.is_nan()) {
  49       fputil::set_errno_if_required(EDOM);
  50       fputil::raise_except_if_required(FE_INVALID);
  51       return fputil::FPBits<float>::quiet_nan().get_val();
  52     }
  53     return static_cast<float>(x);
  54   }
  55
  56   double m = static_cast<double>(xbits.get_exponent());
  57
  58   // Get the 8 highest bits, use 7 bits (excluding the implicit hidden bit) for
  59   // lookup tables.
  60   int f_index = static_cast<int>(xbits.get_mantissa() >>
  61                                  (fputil::FPBits<double>::FRACTION_LEN - 7));
  62
  63   // Set bits to 1.m
  64   xbits.set_biased_exponent(0x3FF);
  65   FPBits f = xbits;
  66
  67   // Clear the lowest 45 bits.
  68   f.set_uintval(f.uintval() & ~0x0000'1FFF'FFFF'FFFFULL);
  69
  70   double d = xbits.get_val() - f.get_val();
  71   d *= ONE_OVER_F[f_index];
  72
  73   double extra_factor = fputil::multiply_add(m, LOG_2, LOG_F[f_index]);
  74
  75   double r = fputil::polyeval(d, extra_factor, 0x1.fffffffffffacp-1,
  76                               -0x1.fffffffef9cb2p-2, 0x1.5555513bc679ap-2,
  77                               -0x1.fff4805ea441p-3, 0x1.930180dbde91ap-3);
  78
  79   return static_cast<float>(r);
  80 }
  81
  82 } // namespace internal
  83
  84 LLVM_LIBC_FUNCTION(float, log1pf, (float x)) {
  85   using FPBits = typename fputil::FPBits<float>;
  86   FPBits xbits(x);
  87   uint32_t x_u = xbits.uintval();
  88   uint32_t x_a = x_u & 0x7fff'ffffU;
  89   double xd = static_cast<double>(x);
  90
  91   // Use log1p(x) = log(1 + x) for |x| > 2^-6;
  92   if (x_a > 0x3c80'0000U) {
  93     // Hard-to-round cases.
  94     switch (x_u) {
  95     case 0x41078febU: // x = 0x1.0f1fd6p3
  96       return fputil::round_result_slightly_up(0x1.1fcbcep1f);
  97     case 0x5cd69e88U: // x = 0x1.ad3d1p+58f
  98       return fputil::round_result_slightly_up(0x1.45c146p+5f);
  99     case 0x65d890d3U: // x = 0x1.b121a6p+76f
 100       return fputil::round_result_slightly_down(0x1.a9a3f2p+5f);
 101     case 0x6f31a8ecU: // x = 0x1.6351d8p+95f
 102       return fputil::round_result_slightly_down(0x1.08b512p+6f);
 103     case 0x7a17f30aU: // x = 0x1.2fe614p+117f
 104       return fputil::round_result_slightly_up(0x1.451436p+6f);
 105     case 0xbd1d20afU: // x = -0x1.3a415ep-5f
 106       return fputil::round_result_slightly_up(-0x1.407112p-5f);
 107     case 0xbf800000U: // x = -1.0
 108       fputil::set_errno_if_required(ERANGE);
 109       fputil::raise_except_if_required(FE_DIVBYZERO);
 110       return FPBits::inf(Sign::NEG).get_val();
 111 #ifndef LIBC_TARGET_CPU_HAS_FMA
 112     case 0x4cc1c80bU: // x = 0x1.839016p+26f
 113       return fputil::round_result_slightly_down(0x1.26fc04p+4f);
 114     case 0x5ee8984eU: // x = 0x1.d1309cp+62f
 115       return fputil::round_result_slightly_up(0x1.5c9442p+5f);
 116     case 0x665e7ca6U: // x = 0x1.bcf94cp+77f
 117       return fputil::round_result_slightly_up(0x1.af66cp+5f);
 118     case 0x79e7ec37U: // x = 0x1.cfd86ep+116f
 119       return fputil::round_result_slightly_up(0x1.43ff6ep+6f);
 120 #endif // LIBC_TARGET_CPU_HAS_FMA
 121     }
 122
 123     return internal::log(xd + 1.0);
 124   }
 125
 126   // |x| <= 2^-6.
 127   // Hard-to round cases.
 128   switch (x_u) {
 129   case 0x35400003U: // x = 0x1.800006p-21f
 130     return fputil::round_result_slightly_down(0x1.7ffffep-21f);
 131   case 0x3710001bU: // x = 0x1.200036p-17f
 132     return fputil::round_result_slightly_down(0x1.1fffe6p-17f);
 133   case 0xb53ffffdU: // x = -0x1.7ffffap-21
 134     return fputil::round_result_slightly_down(-0x1.800002p-21f);
 135   case 0xb70fffe5U: // x = -0x1.1fffcap-17
 136     return fputil::round_result_slightly_down(-0x1.20001ap-17f);
 137   case 0xbb0ec8c4U: // x = -0x1.1d9188p-9
 138     return fputil::round_result_slightly_up(-0x1.1de14ap-9f);
 139   }
 140
 141   // Polymial generated by Sollya with:
 142   // > fpminimax(log(1 + x)/x, 7, [|D...|], [-2^-6; 2^-6]);
 143   const double COEFFS[7] = {-0x1.0000000000000p-1, 0x1.5555555556aadp-2,
 144                             -0x1.000000000181ap-2, 0x1.999998998124ep-3,
 145                             -0x1.55555452e2a2bp-3, 0x1.24adb8cde4aa7p-3,
 146                             -0x1.0019db915ef6fp-3};
 147
 148   double xsq = xd * xd;
 149   double c0 = fputil::multiply_add(xd, COEFFS[1], COEFFS[0]);
 150   double c1 = fputil::multiply_add(xd, COEFFS[3], COEFFS[2]);
 151   double c2 = fputil::multiply_add(xd, COEFFS[5], COEFFS[4]);
 152   double r = fputil::polyeval(xsq, xd, c0, c1, c2, COEFFS[6]);
 153
 154   return static_cast<float>(r);
 155 }
 156
 157 } // namespace LIBC_NAMESPACE_DECL