diff --git a/libc/src/math/generic/logf.cpp b/libc/src/math/generic/logf.cpp
--- a/libc/src/math/generic/logf.cpp
+++ b/libc/src/math/generic/logf.cpp
@@ -9,13 +9,15 @@
 #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:
@@ -101,6 +103,42 @@
   constexpr double LOG_2 = 0x1.62e42fefa39efp-1;
   using FPBits = typename fputil::FPBits<float>;
   FPBits xbits(x);
+
+  switch (FPBits(x).uintval()) {
+  case 0x41178febU:
+    if (fputil::get_round() == FE_TONEAREST)
+      return 0x1.1fcbcep+1f;
+    break;
+  case 0x4c5d65a5U:
+    if (fputil::get_round() == FE_TONEAREST)
+      return 0x1.1e0696p+4f;
+    break;
+  case 0x65d890d3U:
+    if (fputil::get_round() == FE_TONEAREST)
+      return 0x1.a9a3f2p+5f;
+    break;
+  case 0x6f31a8ecU:
+    if (fputil::get_round() == FE_TONEAREST)
+      return 0x1.08b512p+6f;
+    break;
+  case 0x3f800001U:
+    if (fputil::get_round() == FE_UPWARD)
+      return 0x1p-23f;
+    return 0x1.fffffep-24f;
+  case 0x500ffb03U:
+    if (fputil::get_round() != FE_UPWARD)
+      return 0x1.6fdd34p+4f;
+    break;
+  case 0x7a17f30aU:
+    if (fputil::get_round() != FE_UPWARD)
+      return 0x1.451436p+6f;
+    break;
+  case 0x5cd69e88U:
+    if (fputil::get_round() != FE_UPWARD)
+      return 0x1.45c146p+5f;
+    break;
+  }
+
   int m = 0;
 
   if (xbits.uintval() < FPBits::MIN_NORMAL ||
@@ -130,26 +168,14 @@
   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
diff --git a/libc/test/src/math/logf_test.cpp b/libc/test/src/math/logf_test.cpp
--- a/libc/test/src/math/logf_test.cpp
+++ b/libc/test/src/math/logf_test.cpp
@@ -31,13 +31,14 @@
 }
 
 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};
+      0x3f7fffffU, 0x3f800001U, 0x3f800006U, 0x3f800014U, 0x3f80001cU,
+      0x3f80c777U, 0x3f80ce72U, 0x3f80d19fU, 0x3f80f7bfU, 0x3f80fcfeU,
+      0x3f81feb4U, 0x3f83d731U, 0x3f90cb1dU, 0x3fc55379U, 0x3fd364d7U,
+      0x41178febU, 0x4c5d65a5U, 0x4e85f412U, 0x500ffb03U, 0x5cd69e88U,
+      0x65d890d3U, 0x6f31a8ecU, 0x7a17f30aU};
   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);