libc/src/math/generic/logf.cpp

   1 //===-- Single-precision log(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/logf.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/FPBits.h"
  13 #include "src/__support/FPUtil/PolyEval.h"
  14 #include "src/__support/FPUtil/except_value_utils.h"
  15 #include "src/__support/FPUtil/multiply_add.h"
  16 #include "src/__support/common.h"
  17 #include "src/__support/macros/config.h"
  18 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
  19 #include "src/__support/macros/properties/cpu_features.h"
  20
  21 // This is an algorithm for log(x) in single precision which is correctly
  22 // rounded for all rounding modes, based on the implementation of log(x) from
  23 // the RLIBM project at:
  24 // https://people.cs.rutgers.edu/~sn349/rlibm
  25
  26 // Step 1 - Range reduction:
  27 //   For x = 2^m * 1.mant, log(x) = m * log(2) + log(1.m)
  28 //   If x is denormal, we normalize it by multiplying x by 2^23 and subtracting
  29 //   m by 23.
  30
  31 // Step 2 - Another range reduction:
  32 //   To compute log(1.mant), let f be the highest 8 bits including the hidden
  33 // bit, and d be the difference (1.mant - f), i.e. the remaining 16 bits of the
  34 // mantissa. Then we have the following approximation formula:
  35 //   log(1.mant) = log(f) + log(1.mant / f)
  36 //               = log(f) + log(1 + d/f)
  37 //               ~ log(f) + P(d/f)
  38 // since d/f is sufficiently small.
  39 //   log(f) and 1/f are then stored in two 2^7 = 128 entries look-up tables.
  40
  41 // Step 3 - Polynomial approximation:
  42 //   To compute P(d/f), we use a single degree-5 polynomial in double precision
  43 // which provides correct rounding for all but few exception values.
  44 //   For more detail about how this polynomial is obtained, please refer to the
  45 // paper:
  46 //   Lim, J. and Nagarakatte, S., "One Polynomial Approximation to Produce
  47 // Correctly Rounded Results of an Elementary Function for Multiple
  48 // Representations and Rounding Modes", Proceedings of the 49th ACM SIGPLAN
  49 // Symposium on Principles of Programming Languages (POPL-2022), Philadelphia,
  50 // USA, January 16-22, 2022.
  51 // https://people.cs.rutgers.edu/~sn349/papers/rlibmall-popl-2022.pdf
  52
  53 namespace LIBC_NAMESPACE_DECL {
  54
  55 LLVM_LIBC_FUNCTION(float, logf, (float x)) {
  56   constexpr double LOG_2 = 0x1.62e42fefa39efp-1;
  57   using FPBits = typename fputil::FPBits<float>;
  58
  59   FPBits xbits(x);
  60   uint32_t x_u = xbits.uintval();
  61
  62   int m = -FPBits::EXP_BIAS;
  63
  64   using fputil::round_result_slightly_down;
  65   using fputil::round_result_slightly_up;
  66
  67   // Small inputs
  68   if (x_u < 0x4c5d65a5U) {
  69     // Hard-to-round cases.
  70     switch (x_u) {
  71     case 0x3f7f4d6fU: // x = 0x1.fe9adep-1f
  72       return round_result_slightly_up(-0x1.659ec8p-9f);
  73     case 0x41178febU: // x = 0x1.2f1fd6p+3f
  74       return round_result_slightly_up(0x1.1fcbcep+1f);
  75 #ifdef LIBC_TARGET_CPU_HAS_FMA
  76     case 0x3f800000U: // x = 1.0f
  77       return 0.0f;
  78 #else
  79     case 0x1e88452dU: // x = 0x1.108a5ap-66f
  80       return round_result_slightly_up(-0x1.6d7b18p+5f);
  81 #endif // LIBC_TARGET_CPU_HAS_FMA
  82     }
  83     // Subnormal inputs.
  84     if (LIBC_UNLIKELY(x_u < FPBits::min_normal().uintval())) {
  85       if (x == 0.0f) {
  86         // Return -inf and raise FE_DIVBYZERO
  87         fputil::set_errno_if_required(ERANGE);
  88         fputil::raise_except_if_required(FE_DIVBYZERO);
  89         return FPBits::inf(Sign::NEG).get_val();
  90       }
  91       // Normalize denormal inputs.
  92       xbits = FPBits(xbits.get_val() * 0x1.0p23f);
  93       m -= 23;
  94       x_u = xbits.uintval();
  95     }
  96   } else {
  97     // Hard-to-round cases.
  98     switch (x_u) {
  99     case 0x4c5d65a5U: // x = 0x1.bacb4ap+25f
 100       return round_result_slightly_down(0x1.1e0696p+4f);
 101     case 0x65d890d3U: // x = 0x1.b121a6p+76f
 102       return round_result_slightly_down(0x1.a9a3f2p+5f);
 103     case 0x6f31a8ecU: // x = 0x1.6351d8p+95f
 104       return round_result_slightly_down(0x1.08b512p+6f);
 105     case 0x7a17f30aU: // x = 0x1.2fe614p+117f
 106       return round_result_slightly_up(0x1.451436p+6f);
 107 #ifndef LIBC_TARGET_CPU_HAS_FMA
 108     case 0x500ffb03U: // x = 0x1.1ff606p+33f
 109       return round_result_slightly_up(0x1.6fdd34p+4f);
 110     case 0x5cd69e88U: // x = 0x1.ad3d1p+58f
 111       return round_result_slightly_up(0x1.45c146p+5f);
 112     case 0x5ee8984eU: // x = 0x1.d1309cp+62f;
 113       return round_result_slightly_up(0x1.5c9442p+5f);
 114 #endif // LIBC_TARGET_CPU_HAS_FMA
 115     }
 116     // Exceptional inputs.
 117     if (LIBC_UNLIKELY(x_u > FPBits::max_normal().uintval())) {
 118       if (x_u == 0x8000'0000U) {
 119         // Return -inf and raise FE_DIVBYZERO
 120         fputil::set_errno_if_required(ERANGE);
 121         fputil::raise_except_if_required(FE_DIVBYZERO);
 122         return FPBits::inf(Sign::NEG).get_val();
 123       }
 124       if (xbits.is_neg() && !xbits.is_nan()) {
 125         // Return NaN and raise FE_INVALID
 126         fputil::set_errno_if_required(EDOM);
 127         fputil::raise_except_if_required(FE_INVALID);
 128         return FPBits::quiet_nan().get_val();
 129       }
 130       // x is +inf or nan
 131       return x;
 132     }
 133   }
 134
 135 #ifndef LIBC_TARGET_CPU_HAS_FMA
 136   // Returning the correct +0 when x = 1.0 for non-FMA targets with FE_DOWNWARD
 137   // rounding mode.
 138   if (LIBC_UNLIKELY((x_u & 0x007f'ffffU) == 0))
 139     return static_cast<float>(
 140         static_cast<double>(m + xbits.get_biased_exponent()) * LOG_2);
 141 #endif // LIBC_TARGET_CPU_HAS_FMA
 142
 143   uint32_t mant = xbits.get_mantissa();
 144   // Extract 7 leading fractional bits of the mantissa
 145   int index = mant >> 16;
 146   // Add unbiased exponent. Add an extra 1 if the 7 leading fractional bits are
 147   // all 1's.
 148   m += static_cast<int>((x_u + (1 << 16)) >> 23);
 149
 150   // Set bits to 1.m
 151   xbits.set_biased_exponent(0x7F);
 152
 153   float u = xbits.get_val();
 154   double v;
 155 #ifdef LIBC_TARGET_CPU_HAS_FMA
 156   v = static_cast<double>(fputil::multiply_add(u, R[index], -1.0f)); // Exact.
 157 #else
 158   v = fputil::multiply_add(static_cast<double>(u), RD[index], -1.0); // Exact
 159 #endif // LIBC_TARGET_CPU_HAS_FMA
 160
 161   // Degree-5 polynomial approximation of log generated by Sollya with:
 162   // > P = fpminimax(log(1 + x)/x, 4, [|1, D...|], [-2^-8, 2^-7]);
 163   constexpr double COEFFS[4] = {-0x1.000000000fe63p-1, 0x1.555556e963c16p-2,
 164                                 -0x1.000028dedf986p-2, 0x1.966681bfda7f7p-3};
 165   double v2 = v * v; // Exact
 166   double p2 = fputil::multiply_add(v, COEFFS[3], COEFFS[2]);
 167   double p1 = fputil::multiply_add(v, COEFFS[1], COEFFS[0]);
 168   double p0 = LOG_R[index] + v;
 169   double r = fputil::multiply_add(static_cast<double>(m), LOG_2,
 170                                   fputil::polyeval(v2, p0, p1, p2));
 171   return static_cast<float>(r);
 172 }
 173
 174 } // namespace LIBC_NAMESPACE_DECL