[libc][math] Implement acoshf function correctly rounded to all rounding modes.

[lntue]

Summary

Implement acoshf function correctly rounded to all rounding modes.

[zimmermann6]

I cannot apply to main (revision f7c1982), the patch fails.

[lntue]

Sync to HEAD.

[lntue]

In D142781#4087870, @zimmermann6 wrote:

I cannot apply to main (revision f7c1982), the patch fails.

I've sync to revision 024115ab1482 and re-upload the patch. Can you try it again? Thanks.

[zimmermann6]

all exhaustive tests do pass. The performance is a little worse than CORE-MATH and glibc:

zimmerma@biscotte:~/svn/core-math$ LIBM=/localdisk/zimmerma/llvm-project/build/projects/libc/lib/libllvmlibc.a ./perf.sh acoshf
GNU libc version: 2.36
GNU libc release: stable
[####################] 100 %
Ntrial = 20 ; Min = 17.383 + 0.168 clc/call; Median-Min = 0.004 clc/call; Max = 17.769 clc/call;
[####################] 100 %
Ntrial = 20 ; Min = 21.634 + 0.150 clc/call; Median-Min = 0.059 clc/call; Max = 22.014 clc/call;
[####################] 100 %
Ntrial = 20 ; Min = 25.034 + 0.320 clc/call; Median-Min = 0.305 clc/call; Max = 25.602 clc/call;

libc/config/darwin/arm/entrypoints.txt

set(TARGET_LIBM_ENTRYPOINTS
     libc.src.fenv.fesetexceptflag
     libc.src.fenv.fesetround
     libc.src.fenv.feraiseexcept
     libc.src.fenv.fetestexcept
     libc.src.fenv.feupdateenv
 
     # math.h entrypoints
     libc.src.math.acosf
+    libc.src.math.acoshf
     libc.src.math.asinf
     libc.src.math.asinhf
     libc.src.math.atanf
     libc.src.math.atanhf
     libc.src.math.copysign
     libc.src.math.copysignf
     libc.src.math.copysignl
     libc.src.math.ceil

libc/config/linux/aarch64/entrypoints.txt

set(TARGET_LIBM_ENTRYPOINTS
     libc.src.fenv.fesetexceptflag
     libc.src.fenv.fesetround
     libc.src.fenv.feraiseexcept
     libc.src.fenv.fetestexcept
     libc.src.fenv.feupdateenv
 
     # math.h entrypoints
     libc.src.math.acosf
+    libc.src.math.acoshf
     libc.src.math.asin
     libc.src.math.asinf
     libc.src.math.asinhf
     libc.src.math.atanf
     libc.src.math.atanhf    
     libc.src.math.copysign
     libc.src.math.copysignf
     libc.src.math.copysignl

libc/config/linux/x86_64/entrypoints.txt

set(TARGET_LIBM_ENTRYPOINTS
     libc.src.fenv.fesetexceptflag
     libc.src.fenv.fesetround
     libc.src.fenv.feraiseexcept
     libc.src.fenv.fetestexcept
     libc.src.fenv.feupdateenv
 
     # math.h entrypoints
     libc.src.math.acosf
+    libc.src.math.acoshf
     libc.src.math.asin
     libc.src.math.asinf
     libc.src.math.asinhf
     libc.src.math.atanf
     libc.src.math.atanhf
     libc.src.math.copysign
     libc.src.math.copysignf
     libc.src.math.copysignl

libc/config/windows/entrypoints.txt

set(TARGET_LIBM_ENTRYPOINTS
     libc.src.fenv.fesetexceptflag
     libc.src.fenv.fesetround
     libc.src.fenv.feraiseexcept
     libc.src.fenv.fetestexcept
     libc.src.fenv.feupdateenv
 
     # math.h entrypoints
     libc.src.math.acosf
+    libc.src.math.acoshf
     libc.src.math.asin
     libc.src.math.asinf
     libc.src.math.asinhf
     libc.src.math.atanf    
     libc.src.math.atanhf
     libc.src.math.copysign
     libc.src.math.copysignf
     libc.src.math.copysignl

libc/docs/math.rst

 
 Higher Math Functions
 ---------------------
 
 ============== ================ =============== ======================
 <Func>         <Func_f> (float) <Func> (double) <Func_l> (long double)
 ============== ================ =============== ======================
 acos           :green:`XA`
-acosh
+acosh          :green:`XA`
 asin           :green:`XA`
 asinh          :green:`XA`
 atan           :green:`XA`
 atan2
 atanh          :green:`XA`
 cbrt
 cos            :green:`XA`      :green:`XA`
 cosh           :green:`XA`

 
 Accuracy of Higher Math Functions
 =================================
 
 ============== ================ =============== ======================
 <Func>         <Func_f> (float) <Func> (double) <Func_l> (long double)
 ============== ================ =============== ======================
 acos           :green:`XA`
+acosh          :green:`XA`
 asin           :green:`XA`
 asinh          :green:`XA`
 atan           :green:`XA`
 atanh          :green:`XA`
 cos            :green:`XA`      large
 cosh           :green:`XA`
 exp            :green:`XA`
 exp10          :green:`XA`

 
 +--------------+-------------------------------+-------------------------------+-------------------------------------+---------------------------------------------------------------------+
 | <Func>       | Reciprocal throughput (ns)    | Latency (ns)                  | Testing ranges                      | Testing configuration                                               |
 |              +-----------+-------------------+-----------+-------------------+                                     +------------+-------------------------+--------------+---------------+
 |              | 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           |
 +--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
+| acoshf       |        18 |                26 |        73 |                74 | :math:`[1, 21]`                     | 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           |
 +--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
 | asinhf       |        21 |                39 |        77 |                91 | :math:`[-10, 10]`                   | 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           |
 +--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
 | atanhf       |        18 |                66 |        68 |               133 | :math:`[-1, 1]`                     | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA           |
 +--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+

libc/spec/stdc.td

HeaderSpec Math = HeaderSpec<
           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<"asin", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
           FunctionSpec<"atanf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
 
+          FunctionSpec<"acoshf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
           FunctionSpec<"asinhf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
           FunctionSpec<"atanhf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
       ]
   >;
 
   HeaderSpec StdIO = HeaderSpec<
       "stdio.h",
       [

libc/src/math/CMakeLists.txt

HDRS
     fma.h
   DEPENDS
     libc.src.__support.FPUtil.fma
   COMPILE_OPTIONS
     -O3
 )
 
 add_math_entrypoint_object(acosf)
+add_math_entrypoint_object(acoshf)
 
 add_math_entrypoint_object(asin)
 add_math_entrypoint_object(asinf)
 add_math_entrypoint_object(asinhf)
 
 add_math_entrypoint_object(atanf)
 
 add_math_entrypoint_object(atanhf)

libc/src/math/acoshf.h

+//===-- Implementation header for acoshf ------------------------*- 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_ACOSHF_H
+#define LLVM_LIBC_SRC_MATH_ACOSHF_H
+
+namespace __llvm_libc {
+
+float acoshf(float x);
+
+} // namespace __llvm_libc
+
+#endif // LLVM_LIBC_SRC_MATH_ACOSHF_H

libc/src/math/generic/CMakeLists.txt

add_entrypoint_object(
   DEPENDS
     .explogxf
     libc.src.__support.FPUtil.fp_bits
   COMPILE_OPTIONS
     -O3
 )
 
 add_entrypoint_object(
+  acoshf
+  SRCS
+    acoshf.cpp
+  HDRS
+    ../acoshf.h
+  DEPENDS
+    .explogxf
+    libc.src.__support.FPUtil.fenv_impl
+    libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.FPUtil.multiply_add
+    libc.src.__support.FPUtil.polyeval
+    libc.src.__support.FPUtil.sqrt
+  COMPILE_OPTIONS
+    -O3
+)
+
+add_entrypoint_object(
   asinhf
   SRCS
     asinhf.cpp
   HDRS
     ../asinhf.h
   DEPENDS
     .explogxf
     libc.src.__support.FPUtil.fp_bits

libc/src/math/generic/acoshf.cpp

+//===-- Single-precision acosh 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/acoshf.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/math/generic/common_constants.h"
+#include "src/math/generic/explogxf.h"
+
+namespace __llvm_libc {
+
+LLVM_LIBC_FUNCTION(float, acoshf, (float x)) {
+  using FPBits_t = typename fputil::FPBits<float>;
+  FPBits_t xbits(x);
+  uint32_t x_u = xbits.uintval();
+
+  if (unlikely(x < 1.0f)) {
+    // x < 1.
+    fputil::set_except(FE_INVALID);
+    return FPBits_t::build_quiet_nan(0);
+  }
+
+  if (unlikely(x_u >= 0x4f8ffb03)) {
+    // Check for exceptional values.
+    uint32_t x_abs = x_u & FPBits_t::FloatProp::EXP_MANT_MASK;
+    if (unlikely(x_abs >= 0x7f80'0000U)) {
+      // x is +inf or NaN.
+      return x;
+    }
+
+    // Helper functions to set results for exceptional cases.
+    auto round_result_slightly_down = [](float r) -> float {
+      volatile float tmp = r;
+      tmp = tmp - 0x1.0p-25f;
+      return tmp;
+    };
+    auto round_result_slightly_up = [](float r) -> float {
+      volatile float tmp = r;
+      tmp = tmp + 0x1.0p-25f;
+      return tmp;
+    };
+
+    switch (x_u) {
+    case 0x4f8ffb03: // x = 0x1.1ff606p32f
+      return round_result_slightly_up(0x1.6fdd34p4f);
+    case 0x5c569e88: // x = 0x1.ad3d1p57f
+      return round_result_slightly_up(0x1.45c146p5f);
+    case 0x5e68984e: // x = 0x1.d1309cp61f
+      return round_result_slightly_up(0x1.5c9442p5f);
+    case 0x655890d3: // x = 0x1.b121a6p75f
+      return round_result_slightly_down(0x1.a9a3f2p5f);
+    case 0x6eb1a8ec: // x = 0x1.6351d8p94f
+      return round_result_slightly_down(0x1.08b512p6f);
+    case 0x7997f30a: // x = 0x1.2fe614p116f
+      return round_result_slightly_up(0x1.451436p6f);
+    }
+  }
+
+  double x_d = static_cast<double>(x);
+  // acosh(x) = log(x + sqrt(x^2 - 1))
+  return log_eval(x_d + fputil::sqrt(fputil::multiply_add(x_d, x_d, -1.0)));
+}
+
+} // namespace __llvm_libc

libc/test/src/math/CMakeLists.txt

add_fp_unittest(
   DEPENDS
     libc.include.errno
     libc.src.errno.errno
     libc.src.math.asinhf
     libc.src.__support.FPUtil.fp_bits
 )
 
 add_fp_unittest(
+  acoshf_test
+  NEED_MPFR
+  SUITE
+    libc_math_unittests
+  SRCS
+    acoshf_test.cpp
+  DEPENDS
+    libc.include.errno
+    libc.src.errno.errno
+    libc.src.math.acoshf
+    libc.src.__support.FPUtil.fp_bits
+)
+
+add_fp_unittest(
   asinf_test
   NEED_MPFR
   SUITE
     libc_math_unittests
   SRCS
     asinf_test.cpp
   DEPENDS
     libc.include.errno

libc/test/src/math/acoshf_test.cpp

+//===-- Unittests for acoshf ----------------------------------------------===//
+//
+// 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/math/acoshf.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_t = __llvm_libc::fputil::FPBits<float>;
+
+namespace mpfr = __llvm_libc::testing::mpfr;
+
+DECLARE_SPECIAL_CONSTANTS(float)
+
+TEST(LlvmLibcAcoshfTest, SpecialNumbers) {
+  errno = 0;
+
+  EXPECT_FP_EQ(aNaN, __llvm_libc::acoshf(aNaN));
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ(aNaN, __llvm_libc::acoshf(0.0f));
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ(0.0f, __llvm_libc::acoshf(1.0f));
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ(inf, __llvm_libc::acoshf(inf));
+  EXPECT_MATH_ERRNO(0);
+
+  EXPECT_FP_EQ(aNaN, __llvm_libc::acoshf(neg_inf));
+  EXPECT_MATH_ERRNO(0);
+}
+
+TEST(LlvmLibcAcoshfTest, 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_t(v));
+    if (isnan(x) || isinf(x))
+      continue;
+    ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acosh, x,
+                                   __llvm_libc::acoshf(x), 0.5);
+  }
+}
+
+TEST(LlvmLibcAcoshfTest, SpecificBitPatterns) {
+  constexpr int N = 12;
+  constexpr uint32_t INPUTS[N] = {
+      0x3f800000, // x = 1.0f
+      0x45abaf26, // x = 0x1.575e4cp12f
+      0x49d29048, // x = 0x1.a5209p20f
+      0x4bdd65a5, // x = 0x1.bacb4ap24f
+      0x4c803f2c, // x = 0x1.007e58p26f
+      0x4f8ffb03, // x = 0x1.1ff606p32f
+      0x5c569e88, // x = 0x1.ad3d1p57f
+      0x5e68984e, // x = 0x1.d1309cp61f
+      0x655890d3, // x = 0x1.b121a6p75f
+      0x65de7ca6, // x = 0x1.bcf94cp76f
+      0x6eb1a8ec, // x = 0x1.6351d8p94f
+      0x7997f30a, // x = 0x1.2fe614p116f
+  };
+
+  for (int i = 0; i < N; ++i) {
+    float x = float(FPBits_t(INPUTS[i]));
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Acosh, x,
+                                   __llvm_libc::acoshf(x), 0.5);
+  }
+}

libc/test/src/math/exhaustive/CMakeLists.txt

DEPENDS
     libc.include.math
     libc.src.math.tanhf
     libc.src.__support.FPUtil.fp_bits
   LINK_LIBRARIES
     -lpthread
 )
 
 add_fp_unittest(
+  acoshf_test
+  NO_RUN_POSTBUILD
+  NEED_MPFR
+  SUITE
+    libc_math_exhaustive_tests
+  SRCS
+    acoshf_test.cpp
+  DEPENDS
+    .exhaustive_test
+    libc.include.math
+    libc.src.math.acoshf
+    libc.src.__support.FPUtil.fp_bits
+  LINK_LIBRARIES
+    -lpthread
+)
+
+add_fp_unittest(
   asinhf_test
   NO_RUN_POSTBUILD
   NEED_MPFR
   SUITE
     libc_math_exhaustive_tests
   SRCS
     asinhf_test.cpp
   DEPENDS

libc/test/src/math/exhaustive/acoshf_test.cpp

+//===-- Exhaustive test for acoshf ----------------------------------------===//
+//
+// 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 "exhaustive_test.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/math/acoshf.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+
+#include <thread>
+
+using FPBits = __llvm_libc::fputil::FPBits<float>;
+
+namespace mpfr = __llvm_libc::testing::mpfr;
+
+struct LlvmLibcAcoshfExhaustiveTest : 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::Acosh, x,
+                                  __llvm_libc::acoshf(x), 0.5, rounding);
+    } while (bits++ < stop);
+    return result;
+  }
+};
+
+static const int NUM_THREADS = std::thread::hardware_concurrency();
+
+// Range: [1, Inf];
+static const uint32_t POS_START = 0x3f80'0000U;
+static const uint32_t POS_STOP = 0x7f80'0000U;
+
+TEST_F(LlvmLibcAcoshfExhaustiveTest, PostiveRangeRoundNearestTieToEven) {
+  test_full_range(POS_START, POS_STOP, mpfr::RoundingMode::Nearest);
+}
+
+TEST_F(LlvmLibcAcoshfExhaustiveTest, PostiveRangeRoundUp) {
+  test_full_range(POS_START, POS_STOP, mpfr::RoundingMode::Upward);
+}
+
+TEST_F(LlvmLibcAcoshfExhaustiveTest, PostiveRangeRoundDown) {
+  test_full_range(POS_START, POS_STOP, mpfr::RoundingMode::Downward);
+}
+
+TEST_F(LlvmLibcAcoshfExhaustiveTest, PostiveRangeRoundTowardZero) {
+  test_full_range(POS_START, POS_STOP, mpfr::RoundingMode::TowardZero);
+}

libc/utils/MPFRWrapper/MPFRUtils.h

 
 enum class Operation : int {
   // Operations with take a single floating point number as input
   // and produce a single floating point number as output. The input
   // and output floating point numbers are of the same kind.
   BeginUnaryOperationsSingleOutput,
   Abs,
   Acos,
+  Acosh,
   Asin,
   Asinh,
   Atan,
   Atanh,
   Ceil,
   Cos,
   Cosh,
   Exp,

libc/utils/MPFRWrapper/MPFRUtils.cpp

public:
   }
 
   MPFRNumber acos() const {
     MPFRNumber result(*this);
     mpfr_acos(result.value, value, mpfr_rounding);
     return result;
   }
 
+  MPFRNumber acosh() const {
+    MPFRNumber result(*this);
+    mpfr_acosh(result.value, value, mpfr_rounding);
+    return result;
+  }
+
   MPFRNumber asin() const {
     MPFRNumber result(*this);
     mpfr_asin(result.value, value, mpfr_rounding);
     return result;
   }
 
   MPFRNumber asinh() const {
     MPFRNumber result(*this);
     mpfr_asinh(result.value, value, mpfr_rounding);
     return result;
   }
+
   MPFRNumber atan() const {
     MPFRNumber result(*this);
     mpfr_atan(result.value, value, mpfr_rounding);
     return result;
   }
 
   MPFRNumber atanh() const {
     MPFRNumber result(*this);

 unary_operation(Operation op, InputType input, unsigned int precision,
                 RoundingMode rounding) {
   MPFRNumber mpfrInput(input, precision, rounding);
   switch (op) {
   case Operation::Abs:
     return mpfrInput.abs();
   case Operation::Acos:
     return mpfrInput.acos();
+  case Operation::Acosh:
+    return mpfrInput.acosh();
   case Operation::Asin:
     return mpfrInput.asin();
   case Operation::Asinh:
     return mpfrInput.asinh();
   case Operation::Atan:
     return mpfrInput.atan();
   case Operation::Atanh:
     return mpfrInput.atanh();