[libc] Make logf function correctly rounded for all rounding modes.

[lntue]

Summary

Make logf function correctly rounded for all rounding modes.

[zimmermann6]

all exhaustive tests do pass, with all four rounding modes. Maybe put in comment the corresponding input values for the exceptional cases ?

[lntue]

Add hexadecimal floating point values of exceptional inputs to comments.

[lntue]

In D118149#3269663, @zimmermann6 wrote:

all exhaustive tests do pass, with all four rounding modes. Maybe put in comment the corresponding input values for the exceptional cases ?

Done.

libc/src/math/generic/logf.cpp

 //===-- Single-precision log(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/logf.h"
 #include "common_constants.h" // Lookup table for (1/f)
 #include "src/__support/FPUtil/BasicOperations.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
 #include "src/__support/FPUtil/FMA.h"
 #include "src/__support/FPUtil/FPBits.h"
 #include "src/__support/FPUtil/PolyEval.h"
 #include "src/__support/common.h"
 
-// This is a correctly-rounded algorithm for log(x) in single precision with
-// round-to-nearest, tie-to-even mode from the RLIBM project at:
+// This is an algorithm for log(x) in single precision which is correctly
+// rounded for all rounding modes, based on the implementation of log(x) from
+// the RLIBM project at:
 // https://people.cs.rutgers.edu/~sn349/rlibm
 
 // Step 1 - Range reduction:
 //   For x = 2^m * 1.mant, log(x) = m * log(2) + log(1.m)
 //   If x is denormal, we normalize it by multiplying x by 2^23 and subtracting
 //   m by 23.
 
 // Step 2 - Another range reduction:
static constexpr double LOG_F[128] = {
     0x1.58cadb5cd7989p-1, 0x1.5ad404c359f2cp-1, 0x1.5cdb1dc6c1764p-1,
     0x1.5ee02a9241675p-1, 0x1.60e32f44788d8p-1};
 
 INLINE_FMA
 LLVM_LIBC_FUNCTION(float, logf, (float x)) {
   constexpr double LOG_2 = 0x1.62e42fefa39efp-1;
   using FPBits = typename fputil::FPBits<float>;
   FPBits xbits(x);
+
+  switch (FPBits(x).uintval()) {
+  case 0x41178febU: // x = 0x1.2f1fd6p+3f
+    if (fputil::get_round() == FE_TONEAREST)
+      return 0x1.1fcbcep+1f;
+    break;
+  case 0x4c5d65a5U: // x = 0x1.bacb4ap+25f
+    if (fputil::get_round() == FE_TONEAREST)
+      return 0x1.1e0696p+4f;
+    break;
+  case 0x65d890d3U: // x = 0x1.b121a6p+76f
+    if (fputil::get_round() == FE_TONEAREST)
+      return 0x1.a9a3f2p+5f;
+    break;
+  case 0x6f31a8ecU: // x = 0x1.6351d8p+95f
+    if (fputil::get_round() == FE_TONEAREST)
+      return 0x1.08b512p+6f;
+    break;
+  case 0x3f800001U: // x = 0x1.000002p+0f
+    if (fputil::get_round() == FE_UPWARD)
+      return 0x1p-23f;
+    return 0x1.fffffep-24f;
+  case 0x500ffb03U: // x = 0x1.1ff606p+33f
+    if (fputil::get_round() != FE_UPWARD)
+      return 0x1.6fdd34p+4f;
+    break;
+  case 0x7a17f30aU: // x = 0x1.2fe614p+117f
+    if (fputil::get_round() != FE_UPWARD)
+      return 0x1.451436p+6f;
+    break;
+  case 0x5cd69e88U: // x = 0x1.ad3d1p+58f
+    if (fputil::get_round() != FE_UPWARD)
+      return 0x1.45c146p+5f;
+    break;
+  }
+
   int m = 0;
 
   if (xbits.uintval() < FPBits::MIN_NORMAL ||
       xbits.uintval() > FPBits::MAX_NORMAL) {
     if (xbits.is_zero()) {
       return static_cast<float>(FPBits::neg_inf());
     }
     if (xbits.get_sign() && !xbits.is_nan()) {
LLVM_LIBC_FUNCTION(float, logf, (float x)) {
   int f_index = xbits.get_mantissa() >> 16;
 
   FPBits f(xbits.val);
   f.bits &= ~0x0000'FFFF;
 
   double d = static_cast<float>(xbits) - static_cast<float>(f);
   d *= ONE_OVER_F[f_index];
 
+  double extra_factor =
+      fputil::fma(static_cast<double>(m), LOG_2, LOG_F[f_index]);
+
   double r = __llvm_libc::fputil::polyeval(
-      d, 0x1.0000000008169p+0, -0x1.0000004f78405p-1, 0x1.555654d2bc769p-2,
-      -0x1.00a570d090322p-2, 0x1.e158d823f89cap-3);
+      d, extra_factor, 0x1.fffffffffffacp-1, -0x1.fffffffef9cb2p-2,
+      0x1.5555513bc679ap-2, -0x1.fff4805ea441p-3, 0x1.930180dbde91ap-3);
 
-  double extra_factor =
-      __llvm_libc::fputil::fma(static_cast<double>(m), LOG_2, LOG_F[f_index]);
-  switch (FPBits(x).uintval()) {
-  case 0x3f80d19f:
-    return 0x1.a1e82cp-8f;
-  case 0x41178feb:
-    return 0x1.1fcbcep+1f;
-  case 0x4c5d65a5:
-    return 0x1.1e0696p+4f;
-  case 0x65d890d3:
-    return 0x1.a9a3f2p+5f;
-  case 0x6f31a8ec:
-    return 0x1.08b512p+6f;
-  default:
-    return static_cast<float>(__llvm_libc::fputil::fma(d, r, extra_factor));
-  }
+  return static_cast<float>(r);
 }
 
 #pragma clang diagnostic pop
 
 } // namespace __llvm_libc

libc/test/src/math/logf_test.cpp

TEST(LlvmLibcLogfTest, SpecialNumbers) {
   EXPECT_TRUE(FPBits((__llvm_libc::logf(neg_inf))).is_nan());
   EXPECT_FP_EQ(neg_inf, __llvm_libc::logf(0.0f));
   EXPECT_FP_EQ(neg_inf, __llvm_libc::logf(-0.0f));
   EXPECT_TRUE(FPBits(__llvm_libc::logf(-1.0f)).is_nan());
   EXPECT_FP_EQ(zero, __llvm_libc::logf(1.0f));
 }
 
 TEST(LlvmLibcLogfTest, TrickyInputs) {
-  constexpr int N = 24;
+  constexpr int N = 28;
   constexpr uint32_t INPUTS[N] = {
-      0x3509dcf6U, 0x3bf86ef0U, 0x3ca1c99fU, 0x3d13e105U, 0x3f7ff1f2U,
-      0x3f7fffffU, 0x3f800006U, 0x3f800014U, 0x3f80001cU, 0x3f80c777U,
-      0x3f80ce72U, 0x3f80d19fU, 0x3f80f7bfU, 0x3f80fcfeU, 0x3f81feb4U,
-      0x3f83d731U, 0x3f90cb1dU, 0x3fc55379U, 0x3fd364d7U, 0x41178febU,
-      0x4c5d65a5U, 0x4e85f412U, 0x65d890d3U, 0x6f31a8ecU};
+      0x3509dcf6U, /*0x1.13b9ecp-21f*/
+      0x3bf86ef0U, /*0x1.f0ddep-8f*/
+      0x3ca1c99fU, /*0x1.43933ep-6f*/
+      0x3d13e105U, /*0x1.27c20ap-5f*/
+      0x3f7ff1f2U, /*0x1.ffe3e4p-1f*/
+      0x3f7fffffU, /*0x1.fffffep-1f*/
+      0x3f800001U, /*0x1.000002p+0f*/
+      0x3f800006U, /*0x1.00000cp+0f*/
+      0x3f800014U, /*0x1.000028p+0f*/
+      0x3f80001cU, /*0x1.000038p+0f*/
+      0x3f80c777U, /*0x1.018eeep+0f*/
+      0x3f80ce72U, /*0x1.019ce4p+0f*/
+      0x3f80d19fU, /*0x1.01a33ep+0f*/
+      0x3f80f7bfU, /*0x1.01ef7ep+0f*/
+      0x3f80fcfeU, /*0x1.01f9fcp+0f*/
+      0x3f81feb4U, /*0x1.03fd68p+0f*/
+      0x3f83d731U, /*0x1.07ae62p+0f*/
+      0x3f90cb1dU, /*0x1.21963ap+0f*/
+      0x3fc55379U, /*0x1.8aa6f2p+0f*/
+      0x3fd364d7U, /*0x1.a6c9aep+0f*/
+      0x41178febU, /*0x1.2f1fd6p+3f*/
+      0x4c5d65a5U, /*0x1.bacb4ap+25f*/
+      0x4e85f412U, /*0x1.0be824p+30f*/
+      0x500ffb03U, /*0x1.1ff606p+33f*/
+      0x5cd69e88U, /*0x1.ad3d1p+58f*/
+      0x65d890d3U, /*0x1.b121a6p+76f*/
+      0x6f31a8ecU, /*0x1.6351d8p+95f*/
+      0x7a17f30aU, /*0x1.2fe614p+117f*/
+  };
   for (int i = 0; i < N; ++i) {
     float x = float(FPBits(INPUTS[i]));
     EXPECT_MPFR_MATCH(mpfr::Operation::Log, x, __llvm_libc::logf(x), 0.5);
   }
 }
 
 TEST(LlvmLibcLogfTest, InFloatRange) {
   constexpr uint32_t COUNT = 1000000;