diff --git a/libc/src/math/generic/log1p.cpp b/libc/src/math/generic/log1p.cpp
index 43eb8a924aef4..b9c58b843a240 100644
--- a/libc/src/math/generic/log1p.cpp
+++ b/libc/src/math/generic/log1p.cpp
@@ -822,8 +822,8 @@ constexpr Float128 BIG_COEFFS[4]{
     {Sign::NEG, -128, 0x80000000'00000000'00000000'00000000_u128},
 };
 
-LIBC_INLINE double log1p_accurate(int e_x, int index,
-                                  fputil::DoubleDouble m_x) {
+[[maybe_unused]] LIBC_INLINE double log1p_accurate(int e_x, int index,
+                                                   fputil::DoubleDouble m_x) {
   Float128 e_x_f128(static_cast<float>(e_x));
   Float128 sum = fputil::quick_mul(LOG_2, e_x_f128);
   sum = fputil::quick_add(sum, LOG_R1[index]);
@@ -882,7 +882,6 @@ LLVM_LIBC_FUNCTION(double, log1p, (double x)) {
 
   constexpr int EXP_BIAS = FPBits_t::EXP_BIAS;
   constexpr int FRACTION_LEN = FPBits_t::FRACTION_LEN;
-  constexpr uint64_t FRACTION_MASK = FPBits_t::FRACTION_MASK;
   FPBits_t xbits(x);
   uint64_t x_u = xbits.uintval();
 
@@ -954,12 +953,12 @@ LLVM_LIBC_FUNCTION(double, log1p, (double x)) {
   //   |x_dd.lo| < ulp(x_dd.hi)
 
   FPBits_t xhi_bits(x_dd.hi);
+  uint64_t xhi_frac = xhi_bits.get_mantissa();
   x_u = xhi_bits.uintval();
   // Range reduction:
   // Find k such that |x_hi - k * 2^-7| <= 2^-8.
-  int idx =
-      static_cast<int>(((x_u & FRACTION_MASK) + (1ULL << (FRACTION_LEN - 8))) >>
-                       (FRACTION_LEN - 7));
+  int idx = static_cast<int>((xhi_frac + (1ULL << (FRACTION_LEN - 8))) >>
+                             (FRACTION_LEN - 7));
   int x_e = xhi_bits.get_exponent() + (idx >> 7);
   double e_x = static_cast<double>(x_e);
 
@@ -974,17 +973,21 @@ LLVM_LIBC_FUNCTION(double, log1p, (double x)) {
   constexpr double ERR_HI[2] = {0x1.0p-85, 0.0};
   double err_hi = ERR_HI[hi == 0.0];
 
-  // Scaling factior = 2^(-xh_bits.get_exponent())
-  uint64_t s_u = (static_cast<uint64_t>(EXP_BIAS) << (FRACTION_LEN + 1)) -
-                 (x_u & FPBits_t::EXP_MASK);
-  // When the exponent of x is 2^1023, its inverse, 2^(-1023), is subnormal.
-  const double EXPONENT_CORRECTION[2] = {0.0, 0x1.0p-1023};
-  double scaling = FPBits_t(s_u).get_val() + EXPONENT_CORRECTION[s_u == 0];
+  // Scale x_dd by 2^(-xh_bits.get_exponent()).
+  int64_t s_u = static_cast<int64_t>(x_u & FPBits_t::EXP_MASK) -
+                (static_cast<int64_t>(EXP_BIAS) << FRACTION_LEN);
   // Normalize arguments:
   //   1 <= m_dd.hi < 2
   //   |m_dd.lo| < 2^-52.
   // This is exact.
-  fputil::DoubleDouble m_dd{scaling * x_dd.lo, scaling * x_dd.hi};
+  uint64_t m_hi = FPBits_t::one().uintval() | xhi_frac;
+
+  uint64_t m_lo =
+      FPBits_t(x_dd.lo).abs().get_val() > x_dd.hi * 0x1.0p-127
+          ? static_cast<uint64_t>(cpp::bit_cast<int64_t>(x_dd.lo) - s_u)
+          : 0;
+
+  fputil::DoubleDouble m_dd{FPBits_t(m_lo).get_val(), FPBits_t(m_hi).get_val()};
 
   // Perform range reduction:
   //   r * m - 1 = r * (m_dd.hi + m_dd.lo) - 1
diff --git a/libc/test/src/math/smoke/log1p_test.cpp b/libc/test/src/math/smoke/log1p_test.cpp
index eba65f56df739..b98c0f26a8bca 100644
--- a/libc/test/src/math/smoke/log1p_test.cpp
+++ b/libc/test/src/math/smoke/log1p_test.cpp
@@ -13,8 +13,6 @@
 #include "test/UnitTest/FPMatcher.h"
 #include "test/UnitTest/Test.h"
 
-#include <stdint.h>
-
 using LlvmLibcLog1pTest = LIBC_NAMESPACE::testing::FPTest<double>;
 
 TEST_F(LlvmLibcLog1pTest, SpecialNumbers) {
@@ -26,6 +24,9 @@ TEST_F(LlvmLibcLog1pTest, SpecialNumbers) {
   EXPECT_FP_EQ(neg_zero, LIBC_NAMESPACE::log1p(-0.0));
   EXPECT_FP_EQ_WITH_EXCEPTION(neg_inf, LIBC_NAMESPACE::log1p(-1.0),
                               FE_DIVBYZERO);
+
+  EXPECT_FP_EQ(0x1.62c829bf8fd9dp9,
+               LIBC_NAMESPACE::log1p(0x1.9b536cac3a09dp1023));
 }
 
 #ifdef LIBC_TEST_FTZ_DAZ
@@ -36,18 +37,24 @@ TEST_F(LlvmLibcLog1pTest, FTZMode) {
   ModifyMXCSR mxcsr(FTZ);
 
   EXPECT_FP_EQ(0.0, LIBC_NAMESPACE::log1p(min_denormal));
+  EXPECT_FP_EQ(0x1.62c829bf8fd9dp9,
+               LIBC_NAMESPACE::log1p(0x1.9b536cac3a09dp1023));
 }
 
 TEST_F(LlvmLibcLog1pTest, DAZMode) {
   ModifyMXCSR mxcsr(DAZ);
 
   EXPECT_FP_EQ(0.0, LIBC_NAMESPACE::log1p(min_denormal));
+  EXPECT_FP_EQ(0x1.62c829bf8fd9dp9,
+               LIBC_NAMESPACE::log1p(0x1.9b536cac3a09dp1023));
 }
 
 TEST_F(LlvmLibcLog1pTest, FTZDAZMode) {
   ModifyMXCSR mxcsr(FTZ | DAZ);
 
   EXPECT_FP_EQ(0.0, LIBC_NAMESPACE::log1p(min_denormal));
+  EXPECT_FP_EQ(0x1.62c829bf8fd9dp9,
+               LIBC_NAMESPACE::log1p(0x1.9b536cac3a09dp1023));
 }
 
 #endif