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