# [libc-commits] [libc] 463dcc8 - [libc][math] Implement acosf function correctly rounded for all rounding modes.

Tue Ly via libc-commits libc-commits at lists.llvm.org
Fri Sep 9 06:55:40 PDT 2022

```Author: Tue Ly
Date: 2022-09-09T09:55:30-04:00
New Revision: 463dcc8749ed713df858dd1738e472725c8b1b35

URL: https://github.com/llvm/llvm-project/commit/463dcc8749ed713df858dd1738e472725c8b1b35
DIFF: https://github.com/llvm/llvm-project/commit/463dcc8749ed713df858dd1738e472725c8b1b35.diff

LOG: [libc][math] Implement acosf function correctly rounded for all rounding modes.

Implement acosf function correctly rounded for all rounding modes.

We perform range reduction as follows:

- When `|x| < 2^(-10)`, we use cubic Taylor polynomial:
```
acos(x) = pi/2 - asin(x) ~ pi/2 - x - x^3 / 6.
```
- When `2^(-10) <= |x| <= 0.5`, we use the same approximation that is used for `asinf(x)` when `|x| <= 0.5`:
```
acos(x) = pi/2 - asin(x) ~ pi/2 - x - x^3 * P(x^2).
```
- When `0.5 < x <= 1`, we use the double angle formula: `cos(2y) = 1 - 2 * sin^2 (y)` to reduce to:
```
acos(x) = 2 * asin( sqrt( (1 - x)/2 ) )
```
- When `-1 <= x < -0.5`, we reduce to the positive case above using the formula:
```
acos(x) = pi - acos(-x)
```

Performance benchmark using perf tool from the CORE-MATH project on Ryzen 1700:
```
\$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh acosf
GNU libc version: 2.35
GNU libc release: stable
CORE-MATH reciprocal throughput   : 28.613
System LIBC reciprocal throughput : 29.204
LIBC reciprocal throughput        : 24.271

\$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh asinf --latency
GNU libc version: 2.35
GNU libc release: stable
CORE-MATH latency   : 55.554
System LIBC latency : 76.879
LIBC latency        : 62.118
```

Reviewed By: orex, zimmermann6

Differential Revision: https://reviews.llvm.org/D133550

libc/src/math/acosf.h
libc/src/math/generic/acosf.cpp
libc/test/src/math/acosf_test.cpp
libc/test/src/math/exhaustive/acosf_test.cpp

Modified:
libc/config/darwin/arm/entrypoints.txt
libc/config/linux/aarch64/entrypoints.txt
libc/config/linux/x86_64/entrypoints.txt
libc/config/windows/entrypoints.txt
libc/docs/math.rst
libc/spec/stdc.td
libc/src/math/CMakeLists.txt
libc/src/math/generic/CMakeLists.txt
libc/src/math/generic/asinf.cpp
libc/src/math/generic/inv_trigf_utils.h
libc/test/src/math/CMakeLists.txt
libc/test/src/math/exhaustive/CMakeLists.txt
libc/test/src/math/exhaustive/asinf_test.cpp
libc/utils/MPFRWrapper/MPFRUtils.cpp
libc/utils/MPFRWrapper/MPFRUtils.h

Removed:

################################################################################
diff  --git a/libc/config/darwin/arm/entrypoints.txt b/libc/config/darwin/arm/entrypoints.txt
index 433c245e640b5..02331e15d541e 100644
--- a/libc/config/darwin/arm/entrypoints.txt
+++ b/libc/config/darwin/arm/entrypoints.txt
@@ -105,6 +105,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.fenv.feupdateenv

# math.h entrypoints
+    libc.src.math.acosf
libc.src.math.asinf
libc.src.math.atanf
libc.src.math.atanhf

diff  --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
index abc6d77397de3..fc64f1ee94062 100644
--- a/libc/config/linux/aarch64/entrypoints.txt
+++ b/libc/config/linux/aarch64/entrypoints.txt
@@ -149,6 +149,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.fenv.feupdateenv

# math.h entrypoints
+    libc.src.math.acosf
libc.src.math.asinf
libc.src.math.atanf
libc.src.math.atanhf

diff  --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index 60ec5f0748509..b1fb34cafc4c0 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -149,6 +149,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.fenv.feupdateenv

# math.h entrypoints
+    libc.src.math.acosf
libc.src.math.asinf
libc.src.math.atanf
libc.src.math.atanhf

diff  --git a/libc/config/windows/entrypoints.txt b/libc/config/windows/entrypoints.txt
index a6791813cab2d..4bd46c5a3a502 100644
--- a/libc/config/windows/entrypoints.txt
+++ b/libc/config/windows/entrypoints.txt
@@ -106,6 +106,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.fenv.feupdateenv

# math.h entrypoints
+    libc.src.math.acosf
libc.src.math.asinf
libc.src.math.atanf
libc.src.math.atanhf

diff  --git a/libc/docs/math.rst b/libc/docs/math.rst
index 0cbd53329776b..55c8748b20b57 100644
--- a/libc/docs/math.rst
+++ b/libc/docs/math.rst
@@ -116,7 +116,7 @@ Higher Math Functions
============== ================ =============== ======================
<Func>         <Func_f> (float) <Func> (double) <Func_l> (long double)
============== ================ =============== ======================
-acos
+acos           |check|
acosh
asin           |check|
asinh
@@ -154,6 +154,7 @@ Accuracy of Higher Math Functions
============== ================ =============== ======================
<Func>         <Func_f> (float) <Func> (double) <Func_l> (long double)
============== ================ =============== ======================
+acos           |check|
asin           |check|
atan           |check|
atanh          |check|
@@ -204,6 +205,8 @@ Performance
|              +-----------+-------------------+-----------+-------------------+                                     +------------+-------------------------+--------------+---------------+
|              | LLVM libc | Reference (glibc) | LLVM libc | Reference (glibc) |                                     | CPU        | OS                      | Compiler     | Special flags |
+==============+===========+===================+===========+===================+=====================================+============+=========================+==============+===============+
+| acosf        |        24 |                29 |        62 |                77 | :math:`[-1, 1]`                     | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA           |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
| asinf        |        23 |                27 |        62 |                62 | :math:`[-1, 1]`                     | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA           |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
| atanf        |        27 |                29 |        79 |                68 | :math:`[-10, 10]`                   | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA           |

diff  --git a/libc/spec/stdc.td b/libc/spec/stdc.td
--- a/libc/spec/stdc.td
+++ b/libc/spec/stdc.td
@@ -480,6 +480,7 @@ def StdC : StandardSpec<"stdc"> {
FunctionSpec<"sinhf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
FunctionSpec<"tanhf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,

+          FunctionSpec<"acosf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
FunctionSpec<"asinf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
FunctionSpec<"atanf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,

diff  --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt
index 313ff6a226ec1..cb2a507d9fa03 100644
--- a/libc/src/math/CMakeLists.txt
+++ b/libc/src/math/CMakeLists.txt
-O3
)

diff  --git a/libc/src/math/acosf.h b/libc/src/math/acosf.h
new file mode 100644
index 0000000000000..9604fbfa51aeb
--- /dev/null
+++ b/libc/src/math/acosf.h
@@ -0,0 +1,18 @@
+//===-- Implementation header for acosf -------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC_MATH_ACOSF_H
+#define LLVM_LIBC_SRC_MATH_ACOSF_H
+
+namespace __llvm_libc {
+
+float acosf(float x);
+
+} // namespace __llvm_libc
+
+#endif // LLVM_LIBC_SRC_MATH_ACOSF_H

diff  --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index a946ae4437952..ffc06c8239445 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.sqrt
+    .inv_trigf_utils
+  COMPILE_OPTIONS
+    -O3
+)
+
+  acosf
+  SRCS
+    acosf.cpp
+  HDRS
+    ../acosf.h
+  DEPENDS
+    libc.src.__support.FPUtil.except_value_utils
+    libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.FPUtil.polyeval
+    libc.src.__support.FPUtil.sqrt
+    .inv_trigf_utils
COMPILE_OPTIONS
-O3
)

diff  --git a/libc/src/math/generic/acosf.cpp b/libc/src/math/generic/acosf.cpp
new file mode 100644
index 0000000000000..73c93cbaa4530
--- /dev/null
+++ b/libc/src/math/generic/acosf.cpp
@@ -0,0 +1,117 @@
+//===-- Single-precision acos function ------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/math/acosf.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/sqrt.h"
+
+#include <errno.h>
+
+#include "inv_trigf_utils.h"
+
+namespace __llvm_libc {
+
+static constexpr size_t N_EXCEPTS = 4;
+
+// Exceptional values when |x| <= 0.5
+static constexpr fputil::ExceptValues<float, N_EXCEPTS> ACOSF_EXCEPTS = {{
+    // (inputs, RZ output, RU offset, RD offset, RN offset)
+    // x = 0x1.110b46p-26, acosf(x) = 0x1.921fb4p0 (RZ)
+    {0x328885a3, 0x3fc90fda, 1, 0, 1},
+    // x = -0x1.110b46p-26, acosf(x) = 0x1.921fb4p0 (RZ)
+    {0xb28885a3, 0x3fc90fda, 1, 0, 1},
+    // x = 0x1.04c444p-12, acosf(x) = 0x1.920f68p0 (RZ)
+    {0x39826222, 0x3fc907b4, 1, 0, 1},
+    // x = -0x1.04c444p-12, acosf(x) = 0x1.923p0 (RZ)
+    {0xb9826222, 0x3fc91800, 1, 0, 1},
+}};
+
+LLVM_LIBC_FUNCTION(float, acosf, (float x)) {
+  using FPBits = typename fputil::FPBits<float>;
+  FPBits xbits(x);
+  uint32_t x_uint = xbits.uintval();
+  uint32_t x_abs = xbits.uintval() & 0x7fff'ffffU;
+  uint32_t x_sign = x_uint >> 31;
+
+  // |x| <= 0.5
+  if (unlikely(x_abs <= 0x3f00'0000U)) {
+    // |x| < 0x1p-10
+    if (unlikely(x_abs < 0x3a80'0000U)) {
+      // When |x| < 2^-10, we use the following approximation:
+      //   acos(x) = pi/2 - asin(x)
+      //           ~ pi/2 - x - x^3 / 6
+
+      // Check for exceptional values
+      if (auto r = ACOSF_EXCEPTS.lookup(x_uint); unlikely(r.has_value()))
+        return r.value();
+
+      double xd = static_cast<double>(x);
+      return fputil::multiply_add(-0x1.5555555555555p-3 * xd, xd * xd,
+                                  M_MATH_PI_2 - xd);
+    }
+
+    // For |x| <= 0.5, we approximate acosf(x) by:
+    //   acos(x) = pi/2 - asin(x) = pi/2 - x * P(x^2)
+    // Where P(X^2) = Q(X) is a degree-20 minimax even polynomial approximating
+    // asin(x)/x on [0, 0.5] generated by Sollya with:
+    // > Q = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20|],
+    //                 [|1, D...|], [0, 0.5]);
+    double xd = static_cast<double>(x);
+    double xsq = xd * xd;
+    double x3 = xd * xsq;
+    double r = asin_eval(xsq);
+    return fputil::multiply_add(-x3, r, M_MATH_PI_2 - xd);
+  }
+
+  // |x| > 1, return NaNs.
+  if (unlikely(x_abs > 0x3f80'0000U)) {
+    if (x_abs <= 0x7f80'0000U) {
+      errno = EDOM;
+      fputil::set_except(FE_INVALID);
+    }
+    return x +
+           FPBits::build_nan(1 << (fputil::MantissaWidth<float>::VALUE - 1));
+  }
+
+  // When 0.5 < |x| <= 1, we perform range reduction as follow:
+  //
+  // Assume further that 0.5 < x <= 1, and let:
+  //   y = acos(x)
+  // We use the double angle formula:
+  //   x = cos(y) = 1 - 2 sin^2(y/2)
+  // So:
+  //   sin(y/2) = sqrt( (1 - x)/2 )
+  // And hence:
+  //   y = 2 * asin( sqrt( (1 - x)/2 ) )
+  // Let u = (1 - x)/2, then
+  //   acos(x) = 2 * asin( sqrt(u) )
+  // Moreover, since 0.5 < x <= 1,
+  //   0 <= u < 1/4, and 0 <= sqrt(u) < 0.5,
+  // And hence we can reuse the same polynomial approximation of asin(x) when
+  // |x| <= 0.5:
+  //   acos(x) ~ 2 * sqrt(u) * P(u).
+  //
+  // When -1 <= x <= -0.5, we use the identity:
+  //   acos(x) = pi - acos(-x)
+  // which is reduced to the postive case.
+
+  xbits.set_sign(false);
+  double xd = static_cast<double>(xbits.get_val());
+  double u = fputil::multiply_add(-0.5, xd, 0.5);
+  double cv = 2 * fputil::sqrt(u);
+
+  double r3 = asin_eval(u);
+  double r = fputil::multiply_add(cv * u, r3, cv);
+  return x_sign ? M_MATH_PI - r : r;
+}
+
+} // namespace __llvm_libc

diff  --git a/libc/src/math/generic/asinf.cpp b/libc/src/math/generic/asinf.cpp
index 262af0fcbd3bc..7314b3868090b 100644
--- a/libc/src/math/generic/asinf.cpp
+++ b/libc/src/math/generic/asinf.cpp
@@ -16,10 +16,9 @@

#include <errno.h>

-namespace __llvm_libc {
+#include "inv_trigf_utils.h"

-// PI / 2
-constexpr double M_MATH_PI_2 = 0x1.921fb54442d18p+0;
+namespace __llvm_libc {

static constexpr size_t N_EXCEPTS = 2;

@@ -41,14 +40,6 @@ static constexpr fputil::ExceptValues<float, N_EXCEPTS> ASINF_EXCEPTS_HI = {{
{0x3f7741b6, 0x3fa7832a, 1, 0, 0},
}};

-// > Q = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20|],
-//                 [|1, D...|], [0, 0.5]);
-static constexpr double COEFFS[10] = {
-    0x1.5555555540fa1p-3, 0x1.333333512edc2p-4, 0x1.6db6cc1541b31p-5,
-    0x1.f1caff324770ep-6, 0x1.6e43899f5f4f4p-6, 0x1.1f847cf652577p-6,
-    0x1.9b60f47f87146p-7, 0x1.259e2634c494fp-6, -0x1.df946fa875ddp-8,
-    0x1.02311ecf99c28p-5};
-
LLVM_LIBC_FUNCTION(float, asinf, (float x)) {
using FPBits = typename fputil::FPBits<float>;
FPBits xbits(x);
@@ -104,14 +95,9 @@ LLVM_LIBC_FUNCTION(float, asinf, (float x)) {
// little more than 0.5.
double xd = static_cast<double>(x);
double xsq = xd * xd;
-    double x4 = xsq * xsq;
-    double r1 = fputil::polyeval(x4, COEFFS[0], COEFFS[2], COEFFS[4], COEFFS[6],
-                                 COEFFS[8]);
-    double r2 = fputil::polyeval(x4, COEFFS[1], COEFFS[3], COEFFS[5], COEFFS[7],
-                                 COEFFS[9]);
-    double r3 = fputil::multiply_add(xsq, r2, r1);
double x3 = xd * xsq;
+    double r = asin_eval(xsq);
}

// |x| > 1, return NaNs.
@@ -130,6 +116,7 @@ LLVM_LIBC_FUNCTION(float, asinf, (float x)) {
return r.value();

// When |x| > 0.5, we perform range reduction as follow:
+  //
// Assume further that 0.5 < x <= 1, and let:
//   y = asin(x)
// We will use the double angle formula:
@@ -143,27 +130,24 @@ LLVM_LIBC_FUNCTION(float, asinf, (float x)) {
//   pi/4 - y/2 = asin( sqrt( (1 - x)/2 ) )
// Equivalently:
//   asin(x) = y = pi/2 - 2 * asin( sqrt( (1 - x)/2 ) )
-  // Let u = (1 - x)/2, then
-  //   asin(x) = pi/2 - 2 * asin(u)
-  // Moreover, since 0.5 < x <= 1,
+  // Let u = (1 - x)/2, then:
+  //   asin(x) = pi/2 - 2 * asin( sqrt(u) )
+  // Moreover, since 0.5 < x <= 1:
//   0 <= u < 1/4, and 0 <= sqrt(u) < 0.5,
// And hence we can reuse the same polynomial approximation of asin(x) when
// |x| <= 0.5:
-  //   asin(x) = pi/2 - 2 * u * P(u^2),
+  //   asin(x) ~ pi/2 - 2 * sqrt(u) * P(u),

xbits.set_sign(false);
+  double sign = SIGN[x_sign];
double xd = static_cast<double>(xbits.get_val());
double u = fputil::multiply_add(-0.5, xd, 0.5);
-  double cv = -2 * fputil::sqrt(u);
-
-  double usq = u * u;
-  double r1 = fputil::polyeval(usq, COEFFS[0], COEFFS[2], COEFFS[4], COEFFS[6],
-                               COEFFS[8]);
-  double r2 = fputil::polyeval(usq, COEFFS[1], COEFFS[3], COEFFS[5], COEFFS[7],
-                               COEFFS[9]);
-  double r3 = fputil::multiply_add(u, r2, r1);
-  double r = fputil::multiply_add(cv * u, r3, M_MATH_PI_2 + cv);
-  return SIGN[x_sign] * r;
+  double c1 = sign * (-2 * fputil::sqrt(u));
+  double c2 = fputil::multiply_add(sign, M_MATH_PI_2, c1);
+  double c3 = c1 * u;
+
+  double r = asin_eval(u);
}

} // namespace __llvm_libc

diff  --git a/libc/src/math/generic/inv_trigf_utils.h b/libc/src/math/generic/inv_trigf_utils.h
index 32f0ba77d0000..202a4a6be5b16 100644
--- a/libc/src/math/generic/inv_trigf_utils.h
+++ b/libc/src/math/generic/inv_trigf_utils.h
@@ -21,7 +21,8 @@

namespace __llvm_libc {

-// PI / 2
+// PI and PI / 2
+constexpr double M_MATH_PI = 0x1.921fb54442d18p+1;
constexpr double M_MATH_PI_2 = 0x1.921fb54442d18p+0;

// atan table size
@@ -36,7 +37,7 @@ extern const double ATAN_K[5];
// atan(u) + atan(v) = atan((u+v)/(1-uv))

// x should be positive, normal finite value
-inline static double atan_eval(double x) {
+static inline double atan_eval(double x) {
using FPB = fputil::FPBits<double>;
// Added some small value to umin and umax mantissa to avoid possible rounding
// errors.
@@ -89,6 +90,24 @@ inline static double atan_eval(double x) {
return sign ? -result : result;
}

+// > Q = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20|],
+//                 [|1, D...|], [0, 0.5]);
+constexpr double ASIN_COEFFS[10] = {0x1.5555555540fa1p-3, 0x1.333333512edc2p-4,
+                                    0x1.6db6cc1541b31p-5, 0x1.f1caff324770ep-6,
+                                    0x1.6e43899f5f4f4p-6, 0x1.1f847cf652577p-6,
+                                    0x1.9b60f47f87146p-7, 0x1.259e2634c494fp-6,
+                                    -0x1.df946fa875ddp-8, 0x1.02311ecf99c28p-5};
+
+// Evaluate P(x^2) - 1, where P(x^2) ~ asin(x)/x
+static inline double asin_eval(double xsq) {
+  double x4 = xsq * xsq;
+  double r1 = fputil::polyeval(x4, ASIN_COEFFS[0], ASIN_COEFFS[2],
+                               ASIN_COEFFS[4], ASIN_COEFFS[6], ASIN_COEFFS[8]);
+  double r2 = fputil::polyeval(x4, ASIN_COEFFS[1], ASIN_COEFFS[3],
+                               ASIN_COEFFS[5], ASIN_COEFFS[7], ASIN_COEFFS[9]);
+}
+
} // namespace __llvm_libc

#endif // LLVM_LIBC_SRC_MATH_GENERIC_INV_TRIGF_UTILS_H

diff  --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt
index b5669057c0509..0cce635be245b 100644
--- a/libc/test/src/math/CMakeLists.txt
+++ b/libc/test/src/math/CMakeLists.txt
libc.src.__support.FPUtil.fp_bits
)

+  acosf_test
+  NEED_MPFR
+  SUITE
+    libc_math_unittests
+  SRCS
+    acosf_test.cpp
+  DEPENDS
+    libc.include.errno
+    libc.src.errno.errno
+    libc.src.math.acosf
+    libc.src.__support.FPUtil.fp_bits
+)
+
atanf_test
NEED_MPFR

diff  --git a/libc/test/src/math/acosf_test.cpp b/libc/test/src/math/acosf_test.cpp
new file mode 100644
index 0000000000000..fa9653739b09e
--- /dev/null
+++ b/libc/test/src/math/acosf_test.cpp
@@ -0,0 +1,75 @@
+//===-- Unittests for acosf -----------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/math/acosf.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+#include "utils/UnitTest/FPMatcher.h"
+#include "utils/UnitTest/Test.h"
+#include <math.h>
+
+#include <errno.h>
+#include <stdint.h>
+
+using FPBits = __llvm_libc::fputil::FPBits<float>;
+
+namespace mpfr = __llvm_libc::testing::mpfr;
+
+DECLARE_SPECIAL_CONSTANTS(float)
+
+TEST(LlvmLibcAcosfTest, SpecialNumbers) {
+  errno = 0;
+
+  EXPECT_FP_EQ(aNaN, __llvm_libc::acosf(aNaN));
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ(aNaN, __llvm_libc::acosf(inf));
+  EXPECT_MATH_ERRNO(EDOM);
+
+  EXPECT_FP_EQ(aNaN, __llvm_libc::acosf(neg_inf));
+  EXPECT_MATH_ERRNO(EDOM);
+}
+
+TEST(LlvmLibcAcosfTest, InFloatRange) {
+  constexpr uint32_t COUNT = 1000000;
+  constexpr uint32_t STEP = UINT32_MAX / COUNT;
+  for (uint32_t i = 0, v = 0; i <= COUNT; ++i, v += STEP) {
+    float x = float(FPBits(v));
+    if (isnan(x) || isinf(x))
+      continue;
+    ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acos, x,
+                                   __llvm_libc::acosf(x), 0.5);
+  }
+}
+
+TEST(LlvmLibcAcosfTest, SpecificBitPatterns) {
+  constexpr int N = 13;
+  constexpr uint32_t INPUTS[N] = {
+      0x3f000000, // x = 0.5f
+      0x3f3504f3, // x = sqrt(2)/2, FE_DOWNWARD
+      0x3f3504f4, // x = sqrt(2)/2, FE_UPWARD
+      0x3f5db3d7, // x = sqrt(3)/2, FE_DOWNWARD
+      0x3f5db3d8, // x = sqrt(3)/2, FE_UPWARD
+      0x3f800000, // x = 1.0f
+      0x40000000, // x = 2.0f
+      0x328885a3, // x = 0x1.110b46p-26
+      0x39826222, // x = 0x1.04c444p-12
+      0x3d09bf86, // x = 0x1.137f0cp-5f
+      0x3de5fa1e, // x = 0x1.cbf43cp-4f
+      0x3f083a1a, // x = 0x1.107434p-1f
+      0x3f7741b6, // x = 0x1.ee836cp-1f
+  };
+
+  for (int i = 0; i < N; ++i) {
+    float x = float(FPBits(INPUTS[i]));
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acos, x,
+                                   __llvm_libc::acosf(x), 0.5);
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acos, -x,
+                                   __llvm_libc::acosf(-x), 0.5);
+  }
+}

diff  --git a/libc/test/src/math/exhaustive/CMakeLists.txt b/libc/test/src/math/exhaustive/CMakeLists.txt
index 1051e87c40192..819e78922cb1a 100644
--- a/libc/test/src/math/exhaustive/CMakeLists.txt
+++ b/libc/test/src/math/exhaustive/CMakeLists.txt
)
+
+  acosf_test
+  NO_RUN_POSTBUILD
+  NEED_MPFR
+  SUITE
+    libc_math_exhaustive_tests
+  SRCS
+    acosf_test.cpp
+  DEPENDS
+    .exhaustive_test
+    libc.include.math
+    libc.src.math.acosf
+    libc.src.__support.FPUtil.fp_bits
+)

diff  --git a/libc/test/src/math/exhaustive/acosf_test.cpp b/libc/test/src/math/exhaustive/acosf_test.cpp
new file mode 100644
index 0000000000000..019232b328628
--- /dev/null
+++ b/libc/test/src/math/exhaustive/acosf_test.cpp
@@ -0,0 +1,76 @@
+//===-- Exhaustive test for acosf -----------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+//
+//===----------------------------------------------------------------------===//
+
+#include "exhaustive_test.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/math/acosf.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+
+
+using FPBits = __llvm_libc::fputil::FPBits<float>;
+
+namespace mpfr = __llvm_libc::testing::mpfr;
+
+struct LlvmLibcAcosfExhaustiveTest : public LlvmLibcExhaustiveTest<uint32_t> {
+  bool check(uint32_t start, uint32_t stop,
+             mpfr::RoundingMode rounding) override {
+    mpfr::ForceRoundingMode r(rounding);
+    uint32_t bits = start;
+    bool result = true;
+    do {
+      FPBits xbits(bits);
+      float x = float(xbits);
+      result &= EXPECT_MPFR_MATCH(mpfr::Operation::Acos, x,
+                                  __llvm_libc::acosf(x), 0.5, rounding);
+    } while (bits++ < stop);
+    return result;
+  }
+};
+
+
+// Range: [0, Inf];
+static const uint32_t POS_START = 0x0000'0000U;
+static const uint32_t POS_STOP = 0x7f80'0000U;
+
+TEST_F(LlvmLibcAcosfExhaustiveTest, PostiveRangeRoundNearestTieToEven) {
+  test_full_range(POS_START, POS_STOP, mpfr::RoundingMode::Nearest);
+}
+
+TEST_F(LlvmLibcAcosfExhaustiveTest, PostiveRangeRoundUp) {
+  test_full_range(POS_START, POS_STOP, mpfr::RoundingMode::Upward);
+}
+
+TEST_F(LlvmLibcAcosfExhaustiveTest, PostiveRangeRoundDown) {
+  test_full_range(POS_START, POS_STOP, mpfr::RoundingMode::Downward);
+}
+
+TEST_F(LlvmLibcAcosfExhaustiveTest, PostiveRangeRoundTowardZero) {
+  test_full_range(POS_START, POS_STOP, mpfr::RoundingMode::TowardZero);
+}
+
+// Range: [-Inf, 0];
+static const uint32_t NEG_START = 0xb000'0000U;
+static const uint32_t NEG_STOP = 0xff80'0000U;
+
+TEST_F(LlvmLibcAcosfExhaustiveTest, NegativeRangeRoundNearestTieToEven) {
+  test_full_range(NEG_START, NEG_STOP, mpfr::RoundingMode::Nearest);
+}
+
+TEST_F(LlvmLibcAcosfExhaustiveTest, NegativeRangeRoundUp) {
+  test_full_range(NEG_START, NEG_STOP, mpfr::RoundingMode::Upward);
+}
+
+TEST_F(LlvmLibcAcosfExhaustiveTest, NegativeRangeRoundDown) {
+  test_full_range(NEG_START, NEG_STOP, mpfr::RoundingMode::Downward);
+}
+
+TEST_F(LlvmLibcAcosfExhaustiveTest, NegativeRangeRoundTowardZero) {
+  test_full_range(NEG_START, NEG_STOP, mpfr::RoundingMode::TowardZero);
+}

diff  --git a/libc/test/src/math/exhaustive/asinf_test.cpp b/libc/test/src/math/exhaustive/asinf_test.cpp
index fa16acbe27eb2..0c6b5c472653b 100644
--- a/libc/test/src/math/exhaustive/asinf_test.cpp
+++ b/libc/test/src/math/exhaustive/asinf_test.cpp
// Range: [0, Inf];
static const uint32_t POS_START = 0x0000'0000U;
static const uint32_t POS_STOP = 0x7f80'0000U;
-/

-    TEST_F(LlvmLibcAsinfExhaustiveTest, PostiveRangeRoundNearestTieToEven) {
+TEST_F(LlvmLibcAsinfExhaustiveTest, PostiveRangeRoundNearestTieToEven) {
test_full_range(POS_START, POS_STOP, mpfr::RoundingMode::Nearest);
}

diff  --git a/libc/utils/MPFRWrapper/MPFRUtils.cpp b/libc/utils/MPFRWrapper/MPFRUtils.cpp
index 910233e87dda7..0f71357e9302a 100644
--- a/libc/utils/MPFRWrapper/MPFRUtils.cpp
+++ b/libc/utils/MPFRWrapper/MPFRUtils.cpp
@@ -184,6 +184,12 @@ class MPFRNumber {
return result;
}

+  MPFRNumber acos() const {
+    MPFRNumber result(*this);
+    mpfr_acos(result.value, value, mpfr_rounding);
+    return result;
+  }
+
MPFRNumber asin() const {
MPFRNumber result(*this);
mpfr_asin(result.value, value, mpfr_rounding);
@@ -526,6 +532,8 @@ unary_operation(Operation op, InputType input, unsigned int precision,
switch (op) {
case Operation::Abs:
return mpfrInput.abs();
+  case Operation::Acos:
+    return mpfrInput.acos();
case Operation::Asin:
return mpfrInput.asin();
case Operation::Atan:

diff  --git a/libc/utils/MPFRWrapper/MPFRUtils.h b/libc/utils/MPFRWrapper/MPFRUtils.h
index 2f9f6f03d6b30..e8d5ecabf5ac3 100644
--- a/libc/utils/MPFRWrapper/MPFRUtils.h
+++ b/libc/utils/MPFRWrapper/MPFRUtils.h
@@ -25,6 +25,7 @@ enum class Operation : int {
// and output floating point numbers are of the same kind.
BeginUnaryOperationsSingleOutput,
Abs,
+  Acos,
Asin,
Atan,
Atanh,

```