[llvm] [libc][math] Implement double precision expm1 function correctly rounded for all rounding modes. (PR #67048)

via llvm-commits llvm-commits at lists.llvm.org
Wed Sep 27 12:07:00 PDT 2023


https://github.com/lntue updated https://github.com/llvm/llvm-project/pull/67048

>From 4c7b1407b8bdc6e7b52716cd06d866ba8e21a102 Mon Sep 17 00:00:00 2001
From: Tue Ly <lntue at google.com>
Date: Wed, 20 Sep 2023 06:51:43 -0400
Subject: [PATCH 1/2] [libc][math] Implement double precision expm1 function
 correctly rounded for all rounding modes.

---
 libc/config/darwin/arm/entrypoints.txt        |   1 +
 libc/config/linux/aarch64/entrypoints.txt     |   1 +
 libc/config/linux/riscv64/entrypoints.txt     |   1 +
 libc/config/linux/x86_64/entrypoints.txt      |   1 +
 libc/config/windows/entrypoints.txt           |   1 +
 libc/docs/math/index.rst                      |   6 +-
 libc/spec/stdc.td                             |   2 +
 libc/src/__support/FPUtil/FPBits.h            |   6 +-
 .../src/__support/FPUtil/except_value_utils.h |  16 +-
 libc/src/math/CMakeLists.txt                  |   1 +
 libc/src/math/expm1.h                         |  18 +
 libc/src/math/generic/CMakeLists.txt          |  27 +
 libc/src/math/generic/exp.cpp                 |   2 +-
 libc/src/math/generic/expm1.cpp               | 493 ++++++++++++++++++
 libc/src/math/generic/expm1f.cpp              |  16 +-
 libc/test/src/math/CMakeLists.txt             |  14 +
 libc/test/src/math/expm1_test.cpp             | 120 +++++
 libc/test/src/math/smoke/CMakeLists.txt       |  13 +
 libc/test/src/math/smoke/expm1_test.cpp       |  39 ++
 19 files changed, 763 insertions(+), 15 deletions(-)
 create mode 100644 libc/src/math/expm1.h
 create mode 100644 libc/src/math/generic/expm1.cpp
 create mode 100644 libc/test/src/math/expm1_test.cpp
 create mode 100644 libc/test/src/math/smoke/expm1_test.cpp

diff --git a/libc/config/darwin/arm/entrypoints.txt b/libc/config/darwin/arm/entrypoints.txt
index f3d2cabb2c141d1..ecdd2d0624fcf5d 100644
--- a/libc/config/darwin/arm/entrypoints.txt
+++ b/libc/config/darwin/arm/entrypoints.txt
@@ -135,6 +135,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.exp10f
     libc.src.math.exp2
     libc.src.math.exp2f
+    libc.src.math.expm1
     libc.src.math.expm1f
     libc.src.math.fabs
     libc.src.math.fabsf
diff --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
index e0bf9800ec881c2..c0c2433594bbc97 100644
--- a/libc/config/linux/aarch64/entrypoints.txt
+++ b/libc/config/linux/aarch64/entrypoints.txt
@@ -249,6 +249,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.exp10f
     libc.src.math.exp2
     libc.src.math.exp2f
+    libc.src.math.expm1
     libc.src.math.expm1f
     libc.src.math.fabs
     libc.src.math.fabsf
diff --git a/libc/config/linux/riscv64/entrypoints.txt b/libc/config/linux/riscv64/entrypoints.txt
index 2b2f2629f78ce67..a2db3576f80d744 100644
--- a/libc/config/linux/riscv64/entrypoints.txt
+++ b/libc/config/linux/riscv64/entrypoints.txt
@@ -258,6 +258,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.exp10f
     libc.src.math.exp2
     libc.src.math.exp2f
+    libc.src.math.expm1
     libc.src.math.expm1f
     libc.src.math.fabs
     libc.src.math.fabsf
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index dcb8c6231432d35..4880ef5e4f2cee2 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -262,6 +262,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.exp10f
     libc.src.math.exp2
     libc.src.math.exp2f
+    libc.src.math.expm1
     libc.src.math.expm1f
     libc.src.math.fabs
     libc.src.math.fabsf
diff --git a/libc/config/windows/entrypoints.txt b/libc/config/windows/entrypoints.txt
index 26552fe7b07b514..1ee088e399438b7 100644
--- a/libc/config/windows/entrypoints.txt
+++ b/libc/config/windows/entrypoints.txt
@@ -134,6 +134,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.exp10f
     libc.src.math.exp2
     libc.src.math.exp2f
+    libc.src.math.expm1
     libc.src.math.expm1f
     libc.src.math.fabs
     libc.src.math.fabsf
diff --git a/libc/docs/math/index.rst b/libc/docs/math/index.rst
index 4e2ef031ab2444b..77b3c8b99a0c2bc 100644
--- a/libc/docs/math/index.rst
+++ b/libc/docs/math/index.rst
@@ -370,7 +370,7 @@ Higher Math Functions
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
 | exp2l      |         |         |         |         |         |         |         |         |         |         |         |         |
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
-| expm1      |         |         |         |         |         |         |         |         |         |         |         |         |
+| expm1      | |check| | |check| |         | |check| | |check| |         |         | |check| |         |         |         |         |
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
 | expm1f     | |check| | |check| |         | |check| | |check| |         |         | |check| |         |         |         |         |
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
@@ -484,9 +484,9 @@ cos            |check|          large
 cosh           |check|
 erf            |check|
 exp            |check|          |check|
-exp10          |check|
+exp10          |check|          |check|
 exp2           |check|          |check|
-expm1          |check|
+expm1          |check|          |check|
 fma            |check|          |check|
 hypot          |check|          |check|
 log            |check|          |check|
diff --git a/libc/spec/stdc.td b/libc/spec/stdc.td
index 86de59d33feecd4..1e9043b841ff1d8 100644
--- a/libc/spec/stdc.td
+++ b/libc/spec/stdc.td
@@ -439,6 +439,8 @@ def StdC : StandardSpec<"stdc"> {
 
           FunctionSpec<"exp2", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
           FunctionSpec<"exp2f", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
+
+          FunctionSpec<"expm1", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
           FunctionSpec<"expm1f", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
 
           FunctionSpec<"remainderf", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<FloatType>]>,
diff --git a/libc/src/__support/FPUtil/FPBits.h b/libc/src/__support/FPUtil/FPBits.h
index 326211669dce660..163b659d707d1f6 100644
--- a/libc/src/__support/FPUtil/FPBits.h
+++ b/libc/src/__support/FPUtil/FPBits.h
@@ -116,7 +116,7 @@ template <typename T> struct FPBits {
 
   FPBits() : bits(0) {}
 
-  LIBC_INLINE T get_val() const { return cpp::bit_cast<T>(bits); }
+  LIBC_INLINE constexpr T get_val() const { return cpp::bit_cast<T>(bits); }
 
   LIBC_INLINE void set_val(T value) { bits = cpp::bit_cast<UIntType>(value); }
 
@@ -185,6 +185,10 @@ template <typename T> struct FPBits {
     return bits;
   }
 
+  LIBC_INLINE static constexpr FPBits<T> min_normal() {
+    return FPBits<T>(MIN_NORMAL);
+  }
+
   LIBC_INLINE static constexpr T build_nan(UIntType v) {
     FPBits<T> bits = inf();
     bits.set_mantissa(v);
diff --git a/libc/src/__support/FPUtil/except_value_utils.h b/libc/src/__support/FPUtil/except_value_utils.h
index df1b9c74aab2819..70318048643bf04 100644
--- a/libc/src/__support/FPUtil/except_value_utils.h
+++ b/libc/src/__support/FPUtil/except_value_utils.h
@@ -100,15 +100,19 @@ template <typename T, size_t N> struct ExceptValues {
 };
 
 // Helper functions to set results for exceptional cases.
-LIBC_INLINE float round_result_slightly_down(float value_rn) {
-  volatile float tmp = value_rn;
-  tmp = tmp - 0x1.0p-100f;
+template<typename T>
+LIBC_INLINE T round_result_slightly_down(T value_rn) {
+  volatile T tmp = value_rn;
+  constexpr T MIN_NORMAL = FPBits<T>::min_normal().get_val();
+  tmp = tmp - MIN_NORMAL;
   return tmp;
 }
 
-LIBC_INLINE float round_result_slightly_up(float value_rn) {
-  volatile float tmp = value_rn;
-  tmp = tmp + 0x1.0p-100f;
+template <typename T>
+LIBC_INLINE T round_result_slightly_up(T value_rn) {
+  volatile T tmp = value_rn;
+  const T MIN_NORMAL = FPBits<T>::min_normal().get_val();
+  tmp = tmp + MIN_NORMAL;
   return tmp;
 }
 
diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt
index 8b2021cac8239fe..00e0e4e6a583987 100644
--- a/libc/src/math/CMakeLists.txt
+++ b/libc/src/math/CMakeLists.txt
@@ -88,6 +88,7 @@ add_math_entrypoint_object(exp2f)
 add_math_entrypoint_object(exp10)
 add_math_entrypoint_object(exp10f)
 
+add_math_entrypoint_object(expm1)
 add_math_entrypoint_object(expm1f)
 
 add_math_entrypoint_object(fabs)
diff --git a/libc/src/math/expm1.h b/libc/src/math/expm1.h
new file mode 100644
index 000000000000000..7ae354e459feb1f
--- /dev/null
+++ b/libc/src/math/expm1.h
@@ -0,0 +1,18 @@
+//===-- Implementation header for expm1 -------------------------*- C++ -*-===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC_MATH_EXPM1_H
+#define LLVM_LIBC_SRC_MATH_EXPM1_H
+
+namespace __llvm_libc {
+
+double expm1(double x);
+
+} // namespace __llvm_libc
+
+#endif // LLVM_LIBC_SRC_MATH_EXPM1_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 9b092c3d3e7e65f..843349ccdc196a7 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -697,6 +697,33 @@ add_entrypoint_object(
     -O3
 )
 
+add_entrypoint_object(
+  expm1
+  SRCS
+    expm1.cpp
+  HDRS
+    ../expm1.h
+  DEPENDS
+    .common_constants
+    .explogxf
+    libc.src.__support.CPP.bit
+    libc.src.__support.CPP.optional
+    libc.src.__support.FPUtil.dyadic_float
+    libc.src.__support.FPUtil.fenv_impl
+    libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.FPUtil.multiply_add
+    libc.src.__support.FPUtil.nearest_integer
+    libc.src.__support.FPUtil.polyeval
+    libc.src.__support.FPUtil.rounding_mode
+    libc.src.__support.FPUtil.triple_double
+    libc.src.__support.macros.optimization
+    libc.include.errno
+    libc.src.errno.errno
+    libc.include.math
+  COMPILE_OPTIONS
+    -O3
+)
+
 add_entrypoint_object(
   expm1f
   SRCS
diff --git a/libc/src/math/generic/exp.cpp b/libc/src/math/generic/exp.cpp
index c16b461c14ed870..16814e069627864 100644
--- a/libc/src/math/generic/exp.cpp
+++ b/libc/src/math/generic/exp.cpp
@@ -104,7 +104,7 @@ Float128 poly_approx_f128(const Float128 &dx) {
       {false, -132, MType({0xaaaaaaaaaaaaaaab, 0xaaaaaaaaaaaaaaaa})}, // 1/24
       {false, -134, MType({0x8888888888888889, 0x8888888888888888})}, // 1/120
       {false, -137, MType({0x60b60b60b60b60b6, 0xb60b60b60b60b60b})}, // 1/720
-      {false, -140, MType({0x00b00b00b00b00b0, 0xb00b00b00b00b00b})}, // 1/5040
+      {false, -140, MType({0x00d00d00d00d00d0, 0xd00d00d00d00d00d})}, // 1/5040
   };
 
   Float128 p = fputil::polyeval(dx, COEFFS_128[0], COEFFS_128[1], COEFFS_128[2],
diff --git a/libc/src/math/generic/expm1.cpp b/libc/src/math/generic/expm1.cpp
new file mode 100644
index 000000000000000..76befaf7cf37d43
--- /dev/null
+++ b/libc/src/math/generic/expm1.cpp
@@ -0,0 +1,493 @@
+//===-- Double-precision e^x - 1 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/expm1.h"
+#include "common_constants.h" // Lookup tables EXP_M1 and EXP_M2.
+#include "explogxf.h"         // ziv_test_denorm.
+#include "src/__support/CPP/bit.h"
+#include "src/__support/CPP/optional.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/double_double.h"
+#include "src/__support/FPUtil/dyadic_float.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/nearest_integer.h"
+#include "src/__support/FPUtil/rounding_mode.h"
+#include "src/__support/FPUtil/triple_double.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+
+#include <errno.h>
+
+// #define DEBUGDEBUG
+
+#ifdef DEBUGDEBUG
+#include <iomanip>
+#include <iostream>
+#endif
+
+namespace __llvm_libc {
+
+using fputil::DoubleDouble;
+using fputil::TripleDouble;
+using Float128 = typename fputil::DyadicFloat<128>;
+
+// log2(e)
+constexpr double LOG2_E = 0x1.71547652b82fep+0;
+
+// Error bounds:
+// Errors when using double precision.
+// 0x1.8p-63;
+constexpr uint64_t ERR_D = 0x3c08000000000000;
+// Errors when using double-double precision.
+// 0x1.0p-99
+constexpr uint64_t ERR_DD = 0x39c0000000000000;
+
+// -2^-12 * log(2)
+// > a = -2^-12 * log(2);
+// > b = round(a, 30, RN);
+// > c = round(a - b, 30, RN);
+// > d = round(a - b - c, D, RN);
+// Errors < 1.5 * 2^-133
+constexpr double MLOG_2_EXP2_M12_HI = -0x1.62e42ffp-13;
+constexpr double MLOG_2_EXP2_M12_MID = 0x1.718432a1b0e26p-47;
+constexpr double MLOG_2_EXP2_M12_MID_30 = 0x1.718432ap-47;
+constexpr double MLOG_2_EXP2_M12_LO = 0x1.b0e2633fe0685p-79;
+
+// Polynomial approximations with double precision:
+// Return expm1(dx) / x ~ 1 + dx / 2 + dx^2 / 6 + dx^3 / 24.
+// For |dx| < 2^-13 + 2^-30:
+//   | output - expm1(dx) / dx | < 2^-51.
+LIBC_INLINE double poly_approx_d(double dx) {
+  // dx^2
+  double dx2 = dx * dx;
+  // c0 = 1 + dx / 2
+  double c0 = fputil::multiply_add(dx, 0.5, 1.0);
+  // c1 = 1/6 + dx / 24
+  double c1 =
+      fputil::multiply_add(dx, 0x1.5555555555555p-5, 0x1.5555555555555p-3);
+  // p = dx^2 * c1 + c0 = 1 + dx / 2 + dx^2 / 6 + dx^3 / 24
+  double p = fputil::multiply_add(dx2, c1, c0);
+  return p;
+}
+
+// Polynomial approximation with double-double precision:
+// Return expm1(dx) / dx ~ 1 + dx / 2 + dx^2 / 6 + ... + dx^6 / 5040
+// For |dx| < 2^-13 + 2^-30:
+//   | output - expm1(dx) | < 2^-101
+DoubleDouble poly_approx_dd(const DoubleDouble &dx) {
+  // Taylor polynomial.
+  constexpr DoubleDouble COEFFS[] = {
+      {0, 0x1p0},                                      // 1
+      {0, 0x1p-1},                                     // 1/2
+      {0x1.5555555555555p-57, 0x1.5555555555555p-3},   // 1/6
+      {0x1.5555555555555p-59, 0x1.5555555555555p-5},   // 1/24
+      {0x1.1111111111111p-63, 0x1.1111111111111p-7},   // 1/120
+      {-0x1.f49f49f49f49fp-65, 0x1.6c16c16c16c17p-10}, // 1/720
+      {0x1.a01a01a01a01ap-73, 0x1.a01a01a01a01ap-13},  // 1/5040
+  };
+
+  DoubleDouble p = fputil::polyeval(dx, COEFFS[0], COEFFS[1], COEFFS[2],
+                                    COEFFS[3], COEFFS[4], COEFFS[5], COEFFS[6]);
+  return p;
+}
+
+// Polynomial approximation with 128-bit precision:
+// Return (exp(dx) - 1)/dx ~ 1 + dx / 2 + dx^2 / 6 + ... + dx^6 / 5040
+// For |dx| < 2^-13 + 2^-30:
+//   | output - exp(dx) | < 2^-126.
+Float128 poly_approx_f128(const Float128 &dx) {
+  using MType = typename Float128::MantissaType;
+
+  constexpr Float128 COEFFS_128[]{
+      {false, -127, MType({0, 0x8000000000000000})},                  // 1.0
+      {false, -128, MType({0, 0x8000000000000000})},                  // 0.5
+      {false, -130, MType({0xaaaaaaaaaaaaaaab, 0xaaaaaaaaaaaaaaaa})}, // 1/6
+      {false, -132, MType({0xaaaaaaaaaaaaaaab, 0xaaaaaaaaaaaaaaaa})}, // 1/24
+      {false, -134, MType({0x8888888888888889, 0x8888888888888888})}, // 1/120
+      {false, -137, MType({0x60b60b60b60b60b6, 0xb60b60b60b60b60b})}, // 1/720
+      {false, -140, MType({0x00d00d00d00d00d0, 0xd00d00d00d00d00d})}, // 1/5040
+  };
+
+  Float128 p = fputil::polyeval(dx, COEFFS_128[0], COEFFS_128[1], COEFFS_128[2],
+                                COEFFS_128[3], COEFFS_128[4], COEFFS_128[5],
+                                COEFFS_128[6]);
+  return p;
+}
+
+#ifdef DEBUGDEBUG
+std::ostream &operator<<(std::ostream &OS, const Float128 &r) {
+  OS << (r.sign ? "-(" : "(") << r.mantissa.val[0] << " + " << r.mantissa.val[1]
+     << " * 2^64) * 2^" << r.exponent << "\n";
+  return OS;
+}
+
+std::ostream &operator<<(std::ostream &OS, const DoubleDouble &r) {
+  OS << std::hexfloat << r.hi << " + " << r.lo << std::defaultfloat << "\n";
+  return OS;
+}
+#endif
+
+// Compute exp(x) - 1 using 128-bit precision.
+// TODO(lntue): investigate triple-double precision implementation for this
+// step.
+Float128 expm1_f128(double x, double kd, int idx1, int idx2) {
+  using MType = typename Float128::MantissaType;
+  // Recalculate dx:
+
+  double t1 = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact
+  double t2 = kd * MLOG_2_EXP2_M12_MID_30;                     // exact
+  double t3 = kd * MLOG_2_EXP2_M12_LO;                         // Error < 2^-133
+
+  Float128 dx = fputil::quick_add(
+      Float128(t1), fputil::quick_add(Float128(t2), Float128(t3)));
+
+  // TODO: Skip recalculating exp_mid1 and exp_mid2.
+  Float128 exp_mid1 =
+      fputil::quick_add(Float128(EXP2_MID1[idx1].hi),
+                        fputil::quick_add(Float128(EXP2_MID1[idx1].mid),
+                                          Float128(EXP2_MID1[idx1].lo)));
+
+  Float128 exp_mid2 =
+      fputil::quick_add(Float128(EXP2_MID2[idx2].hi),
+                        fputil::quick_add(Float128(EXP2_MID2[idx2].mid),
+                                          Float128(EXP2_MID2[idx2].lo)));
+
+  Float128 exp_mid = fputil::quick_mul(exp_mid1, exp_mid2);
+
+  int hi = static_cast<int>(kd) >> 12;
+  Float128 minus_one{true, -127 - hi, MType({0, 0x8000000000000000})};
+
+  Float128 exp_mid_m1 = fputil::quick_add(exp_mid, minus_one);
+
+  Float128 p = poly_approx_f128(dx);
+
+  // r = exp_mid * (1 + dx * P) - 1
+  //   = (exp_mid - 1) + (dx * exp_mid) * P
+  Float128 r =
+      fputil::multiply_add(fputil::quick_mul(exp_mid, dx), p, exp_mid_m1);
+
+  r.exponent += hi;
+
+#ifdef DEBUGDEBUG
+  std::cout << "=== VERY SLOW PASS ===\n"
+            << "        kd: " << kd << "\n"
+            << "        dx: " << dx << "exp_mid_m1: " << exp_mid_m1
+            << "   exp_mid: " << exp_mid << "         p: " << p
+            << "         r: " << r << std::endl;
+#endif
+
+  return r;
+}
+
+// Compute exp(x) - 1 with double-double precision.
+DoubleDouble exp_double_double(double x, double kd, const DoubleDouble &exp_mid,
+                               const DoubleDouble &hi_part) {
+  // Recalculate dx:
+  //   dx = x - k * 2^-12 * log(2)
+  double t1 = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact
+  double t2 = kd * MLOG_2_EXP2_M12_MID_30;                     // exact
+  double t3 = kd * MLOG_2_EXP2_M12_LO;                         // Error < 2^-130
+
+  DoubleDouble dx = fputil::exact_add(t1, t2);
+  dx.lo += t3;
+
+  // Degree-6 Taylor polynomial approximation in double-double precision.
+  // | p - exp(x) | < 2^-100.
+  DoubleDouble p = poly_approx_dd(dx);
+
+  // Error bounds: 2^-99.
+  DoubleDouble r =
+      fputil::multiply_add(fputil::quick_mult(exp_mid, dx), p, hi_part);
+
+#ifdef DEBUGDEBUG
+  std::cout << "=== SLOW PASS ===\n"
+            << "   dx: " << dx << "    p: " << p << "    r: " << r << std::endl;
+#endif
+
+  return r;
+}
+
+// Check for exceptional cases when
+// |x| <= 2^-53 or x < log(2^-54) or x >= 0x1.6232bdd7abcd3p+9
+double set_exceptional(double x) {
+  using FPBits = typename fputil::FPBits<double>;
+  using FloatProp = typename fputil::FloatProperties<double>;
+  FPBits xbits(x);
+
+  uint64_t x_u = xbits.uintval();
+  uint64_t x_abs = x_u & FloatProp::EXP_MANT_MASK;
+
+  // |x| <= 2^-53.
+  if (x_abs <= 0x3ca0'0000'0000'0000ULL) {
+    // expm1(x) ~ x.
+
+    if (LIBC_UNLIKELY(x_abs <= 0x0370'0000'0000'0000ULL)) {
+      if (LIBC_UNLIKELY(x_abs == 0))
+        return x;
+      // |x| <= 2^-968, need to scale up a bit before rounding, then scale it
+      // back down.
+      return 0x1.0p-200 * fputil::multiply_add(x, 0x1.0p+200, 0x1.0p-1022);
+    }
+
+    // 2^-968 < |x| <= 2^-53.
+    return fputil::round_result_slightly_up(x);
+  }
+
+  // x < log(2^-54) || x >= 0x1.6232bdd7abcd3p+9 or inf/nan.
+
+  // x < log(2^-54) or -inf/nan
+  if (x_u >= 0xc042'b708'8723'20e2ULL) {
+    // expm1(-Inf) = -1
+    if (xbits.is_inf())
+      return -1.0;
+
+    // exp(nan) = nan
+    if (xbits.is_nan())
+      return x;
+
+    return fputil::round_result_slightly_up(-1.0);
+  }
+
+  // x >= round(log(MAX_NORMAL), D, RU) = 0x1.62e42fefa39fp+9 or +inf/nan
+  // x is finite
+  if (x_u < 0x7ff0'0000'0000'0000ULL) {
+    int rounding = fputil::quick_get_round();
+    if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
+      return static_cast<double>(FPBits(FPBits::MAX_NORMAL));
+
+    fputil::set_errno_if_required(ERANGE);
+    fputil::raise_except_if_required(FE_OVERFLOW);
+  }
+  // x is +inf or nan
+  return x + static_cast<double>(FPBits::inf());
+}
+
+LLVM_LIBC_FUNCTION(double, expm1, (double x)) {
+  using FPBits = typename fputil::FPBits<double>;
+  using FloatProp = typename fputil::FloatProperties<double>;
+  FPBits xbits(x);
+
+  bool x_sign = xbits.get_sign();
+  uint64_t x_u = xbits.uintval();
+
+  // Upper bound: max normal number = 2^1023 * (2 - 2^-52)
+  // > round(log (2^1023 ( 2 - 2^-52 )), D, RU) = 0x1.62e42fefa39fp+9
+  // > round(log (2^1023 ( 2 - 2^-52 )), D, RD) = 0x1.62e42fefa39efp+9
+  // > round(log (2^1023 ( 2 - 2^-52 )), D, RN) = 0x1.62e42fefa39efp+9
+  // > round(exp(0x1.62e42fefa39fp+9), D, RN) = infty
+
+  // Lower bound: log(2^-54) = -0x1.2b708872320e2p5
+  // > round(log(2^-54), D, RN) = -0x1.2b708872320e2p5
+
+  // x < log(2^-54) or x >= 0x1.6232bdd7abcd3p+9 or |x| <= 2^-53.
+
+  if (LIBC_UNLIKELY(x_u >= 0xc042b708872320e2 ||
+                    (x_u <= 0xbca0000000000000 && x_u >= 0x40862e42fefa39f0) ||
+                    x_u <= 0x3ca0000000000000)) {
+    return set_exceptional(x);
+  }
+
+  // Now log(2^-54) <= x <= -2^-53 or 2^-53 <= x < log(2^1023 * (2 - 2^-52))
+
+  // Range reduction:
+  // Let x = log(2) * (hi + mid1 + mid2) + lo
+  // in which:
+  //   hi is an integer
+  //   mid1 * 2^6 is an integer
+  //   mid2 * 2^12 is an integer
+  // then:
+  //   exp(x) = 2^hi * 2^(mid1) * 2^(mid2) * exp(lo).
+  // With this formula:
+  //   - multiplying by 2^hi is exact and cheap, simply by adding the exponent
+  //     field.
+  //   - 2^(mid1) and 2^(mid2) are stored in 2 x 64-element tables.
+  //   - exp(lo) ~ 1 + lo + a0 * lo^2 + ...
+  //
+  // They can be defined by:
+  //   hi + mid1 + mid2 = 2^(-12) * round(2^12 * log_2(e) * x)
+  // If we store L2E = round(log2(e), D, RN), then:
+  //   log2(e) - L2E ~ 1.5 * 2^(-56)
+  // So the errors when computing in double precision is:
+  //   | x * 2^12 * log_2(e) - D(x * 2^12 * L2E) | <=
+  //  <= | x * 2^12 * log_2(e) - x * 2^12 * L2E | +
+  //     + | x * 2^12 * L2E - D(x * 2^12 * L2E) |
+  //  <= 2^12 * ( |x| * 1.5 * 2^-56 + eps(x))  for RN
+  //     2^12 * ( |x| * 1.5 * 2^-56 + 2*eps(x)) for other rounding modes.
+  // So if:
+  //   hi + mid1 + mid2 = 2^(-12) * round(x * 2^12 * L2E) is computed entirely
+  // in double precision, the reduced argument:
+  //   lo = x - log(2) * (hi + mid1 + mid2) is bounded by:
+  //   |lo| <= 2^-13 + (|x| * 1.5 * 2^-56 + 2*eps(x))
+  //         < 2^-13 + (1.5 * 2^9 * 1.5 * 2^-56 + 2*2^(9 - 52))
+  //         < 2^-13 + 2^-41
+  //
+
+  // The following trick computes the round(x * L2E) more efficiently
+  // than using the rounding instructions, with the tradeoff for less accuracy,
+  // and hence a slightly larger range for the reduced argument `lo`.
+  //
+  // To be precise, since |x| < |log(2^-1075)| < 1.5 * 2^9,
+  //   |x * 2^12 * L2E| < 1.5 * 2^9 * 1.5 < 2^23,
+  // So we can fit the rounded result round(x * 2^12 * L2E) in int32_t.
+  // Thus, the goal is to be able to use an additional addition and fixed width
+  // shift to get an int32_t representing round(x * 2^12 * L2E).
+  //
+  // Assuming int32_t using 2-complement representation, since the mantissa part
+  // of a double precision is unsigned with the leading bit hidden, if we add an
+  // extra constant C = 2^e1 + 2^e2 with e1 > e2 >= 2^25 to the product, the
+  // part that are < 2^e2 in resulted mantissa of (x*2^12*L2E + C) can be
+  // considered as a proper 2-complement representations of x*2^12*L2E.
+  //
+  // One small problem with this approach is that the sum (x*2^12*L2E + C) in
+  // double precision is rounded to the least significant bit of the dorminant
+  // factor C.  In order to minimize the rounding errors from this addition, we
+  // want to minimize e1.  Another constraint that we want is that after
+  // shifting the mantissa so that the least significant bit of int32_t
+  // corresponds to the unit bit of (x*2^12*L2E), the sign is correct without
+  // any adjustment.  So combining these 2 requirements, we can choose
+  //   C = 2^33 + 2^32, so that the sign bit corresponds to 2^31 bit, and hence
+  // after right shifting the mantissa, the resulting int32_t has correct sign.
+  // With this choice of C, the number of mantissa bits we need to shift to the
+  // right is: 52 - 33 = 19.
+  //
+  // Moreover, since the integer right shifts are equivalent to rounding down,
+  // we can add an extra 0.5 so that it will become round-to-nearest, tie-to-
+  // +infinity.  So in particular, we can compute:
+  //   hmm = x * 2^12 * L2E + C,
+  // where C = 2^33 + 2^32 + 2^-1, then if
+  //   k = int32_t(lower 51 bits of double(x * 2^12 * L2E + C) >> 19),
+  // the reduced argument:
+  //   lo = x - log(2) * 2^-12 * k is bounded by:
+  //   |lo| <= 2^-13 + 2^-41 + 2^-12*2^-19
+  //         = 2^-13 + 2^-31 + 2^-41.
+  //
+  // Finally, notice that k only uses the mantissa of x * 2^12 * L2E, so the
+  // exponent 2^12 is not needed.  So we can simply define
+  //   C = 2^(33 - 12) + 2^(32 - 12) + 2^(-13 - 12), and
+  //   k = int32_t(lower 51 bits of double(x * L2E + C) >> 19).
+
+  // Rounding errors <= 2^-31 + 2^-41.
+  double tmp = fputil::multiply_add(x, LOG2_E, 0x1.8000'0000'4p21);
+  int k = static_cast<int>(cpp::bit_cast<uint64_t>(tmp) >> 19);
+  double kd = static_cast<double>(k);
+
+  uint32_t idx1 = (k >> 6) & 0x3f;
+  uint32_t idx2 = k & 0x3f;
+  int hi = k >> 12;
+
+  DoubleDouble exp_mid1{EXP2_MID1[idx1].mid, EXP2_MID1[idx1].hi};
+  DoubleDouble exp_mid2{EXP2_MID2[idx2].mid, EXP2_MID2[idx2].hi};
+
+  DoubleDouble exp_mid = fputil::quick_mult(exp_mid1, exp_mid2);
+
+  // -2^(-hi)
+  double one_scaled =
+      FPBits::create_value(true, FPBits::EXPONENT_BIAS - hi, 0).get_val();
+
+  // 2^(mid1 + mid2) - 2^(-hi)
+  DoubleDouble hi_part = x_sign ? fputil::exact_add(one_scaled, exp_mid.hi)
+                                : fputil::exact_add(exp_mid.hi, one_scaled);
+
+  hi_part.lo += exp_mid.lo;
+
+  // |x - (hi + mid1 + mid2) * log(2) - dx| < 2^11 * eps(M_LOG_2_EXP2_M12.lo)
+  //                                        = 2^11 * 2^-13 * 2^-52
+  //                                        = 2^-54.
+  // |dx| < 2^-13 + 2^-30.
+  double lo_h = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact
+  double dx = fputil::multiply_add(kd, MLOG_2_EXP2_M12_MID, lo_h);
+
+  // We use the degree-4 Taylor polynomial to approximate exp(lo):
+  //   exp(lo) ~ 1 + lo + lo^2 / 2 + lo^3 / 6 + lo^4 / 24 = 1 + lo * P(lo)
+  // So that the errors are bounded by:
+  //   |P(lo) - expm1(lo)/lo| < |lo|^4 / 64 < 2^(-13 * 4) / 64 = 2^-58
+  // Let P_ be an evaluation of P where all intermediate computations are in
+  // double precision.  Using either Horner's or Estrin's schemes, the evaluated
+  // errors can be bounded by:
+  //      |P_(dx) - P(dx)| < 2^-51
+  //   => |dx * P_(dx) - expm1(lo) | < 1.5 * 2^-64
+  //   => 2^(mid1 + mid2) * |dx * P_(dx) - expm1(lo)| < 1.5 * 2^-63.
+  // Since we approximate
+  //   2^(mid1 + mid2) ~ exp_mid.hi + exp_mid.lo,
+  // We use the expression:
+  //    (exp_mid.hi + exp_mid.lo) * (1 + dx * P_(dx)) ~
+  //  ~ exp_mid.hi + (exp_mid.hi * dx * P_(dx) + exp_mid.lo)
+  // with errors bounded by 1.5 * 2^-63.
+
+  // Finally, we have the following approximation formula:
+  //   expm1(x) = 2^hi * 2^(mid1 + mid2) * exp(lo) - 1
+  //            = 2^hi * ( 2^(mid1 + mid2) * exp(lo) - 2^(-hi) )
+  //            ~ 2^hi * ( (exp_mid.hi - 2^-hi) +
+  //                       + (exp_mid.hi * dx * P_(dx) + exp_mid.lo))
+
+  double mid_lo = dx * exp_mid.hi;
+
+  // Approximate expm1(dx)/dx ~ 1 + dx / 2 + dx^2 / 6 + dx^3 / 24.
+  double p = poly_approx_d(dx);
+
+  double lo = fputil::multiply_add(p, mid_lo, hi_part.lo);
+
+  uint64_t err = x_sign ? (static_cast<uint64_t>(-hi) << 52) : 0;
+
+  double err_d = cpp::bit_cast<double>(ERR_D + err);
+
+  double upper = hi_part.hi + (lo + err_d);
+  double lower = hi_part.hi + (lo - err_d);
+
+#ifdef DEBUGDEBUG
+  std::cout << "=== FAST PASS ===\n"
+            << "      x: " << std::hexfloat << x << std::defaultfloat << "\n"
+            << "      k: " << k << "\n"
+            << "   idx1: " << idx1 << "\n"
+            << "   idx2: " << idx2 << "\n"
+            << "     hi: " << hi << "\n"
+            << "     dx: " << std::hexfloat << dx << std::defaultfloat << "\n"
+            << "exp_mid: " << exp_mid << "hi_part: " << hi_part
+            << " mid_lo: " << std::hexfloat << mid_lo << std::defaultfloat
+            << "\n"
+            << "      p: " << std::hexfloat << p << std::defaultfloat << "\n"
+            << "     lo: " << std::hexfloat << lo << std::defaultfloat << "\n"
+            << "  upper: " << std::hexfloat << upper << std::defaultfloat
+            << "\n"
+            << "  lower: " << std::hexfloat << lower << std::defaultfloat
+            << "\n"
+            << std::endl;
+#endif
+
+  if (LIBC_LIKELY(upper == lower)) {
+    // to multiply by 2^hi, a fast way is to simply add hi to the exponent
+    // field.
+    int64_t exp_hi = static_cast<int64_t>(hi) << FloatProp::MANTISSA_WIDTH;
+    double r = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(upper));
+    return r;
+  }
+
+  // Use double-double
+  DoubleDouble r_dd = exp_double_double(x, kd, exp_mid, hi_part);
+
+  double err_dd = cpp::bit_cast<double>(ERR_DD + err);
+
+  double upper_dd = r_dd.hi + (r_dd.lo + err_dd);
+  double lower_dd = r_dd.hi + (r_dd.lo - err_dd);
+
+  if (LIBC_LIKELY(upper_dd == lower_dd)) {
+    int64_t exp_hi = static_cast<int64_t>(hi) << FloatProp::MANTISSA_WIDTH;
+    double r = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(upper_dd));
+    return r;
+  }
+
+  // Use 128-bit precision
+  Float128 r_f128 = expm1_f128(x, kd, idx1, idx2);
+
+  return static_cast<double>(r_f128);
+}
+
+} // namespace __llvm_libc
diff --git a/libc/src/math/generic/expm1f.cpp b/libc/src/math/generic/expm1f.cpp
index 811baec0e91038f..0d384a20e5a79a9 100644
--- a/libc/src/math/generic/expm1f.cpp
+++ b/libc/src/math/generic/expm1f.cpp
@@ -111,16 +111,24 @@ LLVM_LIBC_FUNCTION(float, expm1f, (float x)) {
 #endif // LIBC_TARGET_CPU_HAS_FMA
     }
 
+    constexpr double COEFFS[] = {
+        0x1p-1, 0x1.55555555557ddp-3, 0x1.55555555552fap-5,
+                         0x1.111110fcd58b7p-7, 0x1.6c16c1717660bp-10,
+                         0x1.a0241f0006d62p-13, 0x1.a01e3f8d3c06p-16
+    };
+
     // 2^-25 <= |x| < 2^-4
     double xd = static_cast<double>(x);
     double xsq = xd * xd;
     // Degree-8 minimax polynomial generated by Sollya with:
     // > display = hexadecimal;
     // > P = fpminimax((expm1(x) - x)/x^2, 6, [|D...|], [-2^-4, 2^-4]);
-    double r =
-        fputil::polyeval(xd, 0x1p-1, 0x1.55555555557ddp-3, 0x1.55555555552fap-5,
-                         0x1.111110fcd58b7p-7, 0x1.6c16c1717660bp-10,
-                         0x1.a0241f0006d62p-13, 0x1.a01e3f8d3c06p-16);
+    
+    double c0 = fputil::multiply_add(xd, COEFFS[1], COEFFS[0]);
+    double c1 = fputil::multiply_add(xd, COEFFS[3], COEFFS[2]);
+    double c2 = fputil::multiply_add(xd, COEFFS[5], COEFFS[4]);
+
+    double r = fputil::polyeval(xsq, c0, c1, c2, COEFFS[6]);
     return static_cast<float>(fputil::multiply_add(r, xsq, xd));
   }
 
diff --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt
index d47e0e0ea4aad6e..2ba03676a633fff 100644
--- a/libc/test/src/math/CMakeLists.txt
+++ b/libc/test/src/math/CMakeLists.txt
@@ -1322,6 +1322,20 @@ add_fp_unittest(
     libc.src.__support.FPUtil.fp_bits
 )
 
+add_fp_unittest(
+ expm1_test
+ NEED_MPFR
+ SUITE
+   libc-math-unittests
+ SRCS
+   expm1_test.cpp
+ DEPENDS
+   libc.src.errno.errno
+   libc.include.math
+   libc.src.math.expm1
+   libc.src.__support.FPUtil.fp_bits
+)
+
 add_fp_unittest(
  log_test
  NEED_MPFR
diff --git a/libc/test/src/math/expm1_test.cpp b/libc/test/src/math/expm1_test.cpp
new file mode 100644
index 000000000000000..abec550b91072e1
--- /dev/null
+++ b/libc/test/src/math/expm1_test.cpp
@@ -0,0 +1,120 @@
+//===-- Unittests for e^x - 1 ---------------------------------------------===//
+//
+// 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/__support/FPUtil/FPBits.h"
+#include "src/errno/libc_errno.h"
+#include "src/math/expm1.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+#include <math.h>
+
+#include <errno.h>
+#include <stdint.h>
+
+namespace mpfr = __llvm_libc::testing::mpfr;
+using __llvm_libc::testing::tlog;
+
+DECLARE_SPECIAL_CONSTANTS(double)
+
+TEST(LlvmLibcExpm1Test, TrickyInputs) {
+  constexpr int N = 21;
+  constexpr uint64_t INPUTS[N] = {
+      0x3FD79289C6E6A5C0,
+      0x3FD05DE80A173EA0, // 0x1.05de80a173eap-2
+      0xbf1eb7a4cb841fcc, // -0x1.eb7a4cb841fccp-14
+      0xbf19a61fb925970d,
+      0x3fda7b764e2cf47a, // 0x1.a7b764e2cf47ap-2
+      0xc04757852a4b93aa, // -0x1.757852a4b93aap+5
+      0x4044c19e5712e377, // x=0x1.4c19e5712e377p+5
+      0xbf19a61fb925970d, // x=-0x1.9a61fb925970dp-14
+      0xc039a74cdab36c28, // x=-0x1.9a74cdab36c28p+4
+      0xc085b3e4e2e3bba9, // x=-0x1.5b3e4e2e3bba9p+9
+      0xc086960d591aec34, // x=-0x1.6960d591aec34p+9
+      0xc086232c09d58d91, // x=-0x1.6232c09d58d91p+9
+      0xc0874910d52d3051, // x=-0x1.74910d52d3051p9
+      0xc0867a172ceb0990, // x=-0x1.67a172ceb099p+9
+      0xc08ff80000000000, // x=-0x1.ff8p+9
+      0xbc971547652b82fe, // x=-0x1.71547652b82fep-54
+      0xbce465655f122ff6, // x=-0x1.465655f122ff6p-49
+      0x3d1bc8ee6b28659a, // x=0x1.bc8ee6b28659ap-46
+      0x3f18442b169f672d, // x=0x1.8442b169f672dp-14
+      0xc02b4f0cfb15ca0f, // x=-0x1.b4f0cfb15ca0fp+3
+      0xc042b708872320dd, // x=-0x1.2b708872320ddp+5
+  };
+  for (int i = 0; i < N; ++i) {
+    double x = double(FPBits(INPUTS[i]));
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Expm1, x,
+                                   __llvm_libc::expm1(x), 0.5);
+  }
+}
+
+TEST(LlvmLibcExpm1Test, InDoubleRange) {
+  constexpr uint64_t COUNT = 1'231;
+  uint64_t START = __llvm_libc::fputil::FPBits<double>(0.25).uintval();
+  uint64_t STOP = __llvm_libc::fputil::FPBits<double>(4.0).uintval();
+  uint64_t STEP = (STOP - START) / COUNT;
+
+  auto test = [&](mpfr::RoundingMode rounding_mode) {
+    mpfr::ForceRoundingMode __r(rounding_mode);
+    if (!__r.success)
+      return;
+
+    uint64_t fails = 0;
+    uint64_t count = 0;
+    uint64_t cc = 0;
+    double mx, mr = 0.0;
+    double tol = 0.5;
+
+    for (uint64_t i = 0, v = START; i <= COUNT; ++i, v += STEP) {
+      double x = FPBits(v).get_val();
+      if (isnan(x) || isinf(x) || x < 0.0)
+        continue;
+      libc_errno = 0;
+      double result = __llvm_libc::expm1(x);
+      ++cc;
+      if (isnan(result) || isinf(result))
+        continue;
+
+      ++count;
+
+      if (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Expm1, x, result,
+                                             0.5, rounding_mode)) {
+        ++fails;
+        while (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Expm1, x,
+                                                  result, tol, rounding_mode)) {
+          mx = x;
+          mr = result;
+
+          if (tol > 1000.0)
+            break;
+
+          tol *= 2.0;
+        }
+      }
+    }
+    tlog << " Expm1 failed: " << fails << "/" << count << "/" << cc
+         << " tests.\n";
+    tlog << "   Max ULPs is at most: " << static_cast<uint64_t>(tol) << ".\n";
+    if (fails) {
+      EXPECT_MPFR_MATCH(mpfr::Operation::Expm1, mx, mr, 0.5, rounding_mode);
+    }
+  };
+
+  tlog << " Test Rounding To Nearest...\n";
+  test(mpfr::RoundingMode::Nearest);
+
+  tlog << " Test Rounding Downward...\n";
+  test(mpfr::RoundingMode::Downward);
+
+  tlog << " Test Rounding Upward...\n";
+  test(mpfr::RoundingMode::Upward);
+
+  tlog << " Test Rounding Toward Zero...\n";
+  test(mpfr::RoundingMode::TowardZero);
+}
diff --git a/libc/test/src/math/smoke/CMakeLists.txt b/libc/test/src/math/smoke/CMakeLists.txt
index 803f6d2b9389bbb..a9b31eaf6a4944c 100644
--- a/libc/test/src/math/smoke/CMakeLists.txt
+++ b/libc/test/src/math/smoke/CMakeLists.txt
@@ -1216,6 +1216,19 @@ add_fp_unittest(
     libc.src.__support.FPUtil.fp_bits
 )
 
+add_fp_unittest(
+  expm1_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    expm1_test.cpp
+  DEPENDS
+    libc.src.errno.errno
+    libc.include.math
+    libc.src.math.expm1
+    libc.src.__support.FPUtil.fp_bits
+)
+
 add_fp_unittest(
   log_test
   SUITE
diff --git a/libc/test/src/math/smoke/expm1_test.cpp b/libc/test/src/math/smoke/expm1_test.cpp
new file mode 100644
index 000000000000000..502a9390fa63582
--- /dev/null
+++ b/libc/test/src/math/smoke/expm1_test.cpp
@@ -0,0 +1,39 @@
+//===-- Unittests for e^x - 1 ---------------------------------------------===//
+//
+// 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/__support/FPUtil/FPBits.h"
+#include "src/errno/libc_errno.h"
+#include "src/math/expm1.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+#include <math.h>
+
+#include <errno.h>
+#include <stdint.h>
+
+namespace mpfr = __llvm_libc::testing::mpfr;
+using __llvm_libc::testing::tlog;
+
+DECLARE_SPECIAL_CONSTANTS(double)
+
+TEST(LlvmLibcExpm1Test, SpecialNumbers) {
+  EXPECT_FP_EQ(aNaN, __llvm_libc::expm1(aNaN));
+  EXPECT_FP_EQ(inf, __llvm_libc::expm1(inf));
+  EXPECT_FP_EQ_ALL_ROUNDING(-1.0, __llvm_libc::expm1(neg_inf));
+  EXPECT_FP_EQ_WITH_EXCEPTION(inf, __llvm_libc::expm1(0x1.0p20), FE_OVERFLOW);
+  EXPECT_FP_EQ_ALL_ROUNDING(zero, __llvm_libc::expm1(zero));
+  EXPECT_FP_EQ_ALL_ROUNDING(neg_zero, __llvm_libc::expm1(neg_zero));
+  // |x| < 2^-53, expm1(x) = x
+  EXPECT_FP_EQ(-0x1.23456789abcdep-55,
+               __llvm_libc::expm1(-0x1.23456789abcdep-55));
+  EXPECT_FP_EQ(0x1.23456789abcdep-55,
+               __llvm_libc::expm1(0x1.23456789abcdep-55));
+  // log(2^-54)
+  EXPECT_FP_EQ(0x1.23456789a, __llvm_libc::expm1(-0x1.2b708872320e2p5));
+}

>From 0b9a9151bdc61df1e613da5a14da8d68ddaa1ccd Mon Sep 17 00:00:00 2001
From: Tue Ly <lntue.h at gmail.com>
Date: Wed, 27 Sep 2023 19:05:22 +0000
Subject: [PATCH 2/2] Update comments on test values and add bazel target for
 expm1.

---
 libc/test/src/math/expm1_test.cpp                | 12 ++++++------
 .../bazel/llvm-project-overlay/libc/BUILD.bazel  | 16 ++++++++++++++++
 2 files changed, 22 insertions(+), 6 deletions(-)

diff --git a/libc/test/src/math/expm1_test.cpp b/libc/test/src/math/expm1_test.cpp
index abec550b91072e1..892fc409b303e55 100644
--- a/libc/test/src/math/expm1_test.cpp
+++ b/libc/test/src/math/expm1_test.cpp
@@ -25,12 +25,12 @@ DECLARE_SPECIAL_CONSTANTS(double)
 TEST(LlvmLibcExpm1Test, TrickyInputs) {
   constexpr int N = 21;
   constexpr uint64_t INPUTS[N] = {
-      0x3FD79289C6E6A5C0,
-      0x3FD05DE80A173EA0, // 0x1.05de80a173eap-2
-      0xbf1eb7a4cb841fcc, // -0x1.eb7a4cb841fccp-14
-      0xbf19a61fb925970d,
-      0x3fda7b764e2cf47a, // 0x1.a7b764e2cf47ap-2
-      0xc04757852a4b93aa, // -0x1.757852a4b93aap+5
+      0x3FD79289C6E6A5C0, // x=0x1.79289c6e6a5cp-2
+      0x3FD05DE80A173EA0, // x=0x1.05de80a173eap-2
+      0xbf1eb7a4cb841fcc, // x=-0x1.eb7a4cb841fccp-14
+      0xbf19a61fb925970d, // x=-0x1.9a61fb925970dp-14
+      0x3fda7b764e2cf47a, // x=0x1.a7b764e2cf47ap-2
+      0xc04757852a4b93aa, // x=-0x1.757852a4b93aap+5
       0x4044c19e5712e377, // x=0x1.4c19e5712e377p+5
       0xbf19a61fb925970d, // x=-0x1.9a61fb925970dp-14
       0xc039a74cdab36c28, // x=-0x1.9a74cdab36c28p+4
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index 80ea75ecd8760e0..a795c1254d539cc 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -1278,6 +1278,22 @@ libc_math_function(
     ],
 )
 
+libc_math_function(
+    name = "expm1",
+    additional_deps = [
+        ":__support_fputil_double_double",
+        ":__support_fputil_dyadic_float",
+        ":__support_fputil_multiply_add",
+        ":__support_fputil_nearest_integer",
+        ":__support_fputil_polyeval",
+        ":__support_fputil_rounding_mode",
+        ":__support_fputil_triple_double",
+        ":__support_macros_optimization",
+        ":common_constants",
+        ":explogxf",
+    ],
+)
+
 libc_math_function(
     name = "expm1f",
     additional_deps = [



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