[libc][math] Added atanf function.

Performance by core-math (core-math/glibc 2.31/current llvm-14):
28.879/20.843/20.15

Differential Revision: https://reviews.llvm.org/D132842
This commit is contained in:
Kirill Okhotnikov 2022-08-29 12:34:15 +02:00
parent 6c1fc7e430
commit 77e1d9beed
22 changed files with 476 additions and 4 deletions

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@ -105,6 +105,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.fenv.feupdateenv libc.src.fenv.feupdateenv
# math.h entrypoints # math.h entrypoints
libc.src.math.atanf
libc.src.math.atanhf libc.src.math.atanhf
libc.src.math.copysign libc.src.math.copysign
libc.src.math.copysignf libc.src.math.copysignf

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@ -149,6 +149,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.fenv.feupdateenv libc.src.fenv.feupdateenv
# math.h entrypoints # math.h entrypoints
libc.src.math.atanf
libc.src.math.atanhf libc.src.math.atanhf
libc.src.math.copysign libc.src.math.copysign
libc.src.math.copysignf libc.src.math.copysignf

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@ -149,7 +149,8 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.fenv.feupdateenv libc.src.fenv.feupdateenv
# math.h entrypoints # math.h entrypoints
libc.src.math.atanhf libc.src.math.atanf
libc.src.math.atanhf
libc.src.math.copysign libc.src.math.copysign
libc.src.math.copysignf libc.src.math.copysignf
libc.src.math.copysignl libc.src.math.copysignl

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@ -106,6 +106,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.fenv.feupdateenv libc.src.fenv.feupdateenv
# math.h entrypoints # math.h entrypoints
libc.src.math.atanf
libc.src.math.atanhf libc.src.math.atanhf
libc.src.math.copysign libc.src.math.copysign
libc.src.math.copysignf libc.src.math.copysignf

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@ -480,7 +480,9 @@ def StdC : StandardSpec<"stdc"> {
FunctionSpec<"sinhf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>, FunctionSpec<"sinhf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
FunctionSpec<"tanhf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>, FunctionSpec<"tanhf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
FunctionSpec<"atanhf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>, FunctionSpec<"atanf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
FunctionSpec<"atanhf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
] ]
>; >;

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@ -196,6 +196,15 @@ template <typename T> struct FPBits {
} }
return result; return result;
} }
inline static FPBits<T> create_value(bool sign, UIntType unbiased_exp,
UIntType mantissa) {
FPBits<T> result;
result.set_sign(sign);
result.set_unbiased_exponent(unbiased_exp);
result.set_mantissa(mantissa);
return result;
}
}; };
} // namespace fputil } // namespace fputil

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@ -184,6 +184,15 @@ template <> struct FPBits<long double> {
bits.set_mantissa(v); bits.set_mantissa(v);
return bits; return bits;
} }
inline static FPBits<long double>
create_value(bool sign, UIntType unbiased_exp, UIntType mantissa) {
FPBits<long double> result;
result.set_sign(sign);
result.set_unbiased_exponent(unbiased_exp);
result.set_mantissa(mantissa);
return result;
}
}; };
static_assert( static_assert(

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@ -66,6 +66,7 @@ add_entrypoint_object(
-O3 -O3
) )
add_math_entrypoint_object(atanf)
add_math_entrypoint_object(atanhf) add_math_entrypoint_object(atanhf)
add_math_entrypoint_object(ceil) add_math_entrypoint_object(ceil)

18
libc/src/math/atanf.h Normal file
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@ -0,0 +1,18 @@
//===-- Implementation header for atanf -------------------------*- 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_ATANF_H
#define LLVM_LIBC_SRC_MATH_ATANF_H
namespace __llvm_libc {
float atanf(float x);
} // namespace __llvm_libc
#endif // LLVM_LIBC_SRC_MATH_ATANF_H

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@ -1242,3 +1242,28 @@ add_entrypoint_object(
-O3 -O3
) )
add_object_library(
inv_trigf_utils
HDRS
inv_trigf_utils.h
SRCS
inv_trigf_utils.cpp
)
add_entrypoint_object(
atanf
SRCS
atanf.cpp
HDRS
../atanf.h
DEPENDS
.inv_trigf_utils
libc.src.__support.FPUtil.fputil
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.nearest_integer
libc.src.__support.FPUtil.polyeval
libc.include.math
COMPILE_OPTIONS
-O3
)

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@ -0,0 +1,57 @@
//===-- Single-precision atan 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/atanf.h"
#include "math_utils.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/math/generic/inv_trigf_utils.h"
namespace __llvm_libc {
LLVM_LIBC_FUNCTION(float, atanf, (float x)) {
using FPBits = typename fputil::FPBits<float>;
FPBits xbits(x);
bool sign = xbits.get_sign();
xbits.set_sign(false);
if (unlikely(xbits.is_inf_or_nan())) {
if (xbits.is_inf())
return opt_barrier(sign ? -M_MATH_PI_2 : M_MATH_PI_2);
else
return x + 1.0f;
}
// |x| == 0.06905200332403183
if (unlikely(xbits.uintval() == 0x3d8d6b23U)) {
if (fputil::get_round() == FE_TONEAREST) {
// 0.06894256919622421
FPBits br(0x3d8d31c3U);
br.set_sign(sign);
return br.get_val();
}
}
// |x| == 1.8670953512191772
if (unlikely(xbits.uintval() == 0x3feefcfbU)) {
int rounding_mode = fputil::get_round();
if (sign) {
if (rounding_mode == FE_DOWNWARD) {
// -1.0790828466415405
return FPBits(0xbf8a1f63U).get_val();
}
} else {
if (rounding_mode == FE_UPWARD) {
// 1.0790828466415405
return FPBits(0x3f8a1f63U).get_val();
}
}
}
return atan_eval(x);
}
} // namespace __llvm_libc

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@ -9,7 +9,6 @@
#ifndef LLVM_LIBC_SRC_MATH_GENERIC_EXPLOGXF_H #ifndef LLVM_LIBC_SRC_MATH_GENERIC_EXPLOGXF_H
#define LLVM_LIBC_SRC_MATH_GENERIC_EXPLOGXF_H #define LLVM_LIBC_SRC_MATH_GENERIC_EXPLOGXF_H
#include "common_constants.h" // Lookup tables EXP_M
#include "math_utils.h" #include "math_utils.h"
#include "src/__support/FPUtil/FEnvImpl.h" #include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h" #include "src/__support/FPUtil/FPBits.h"

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@ -0,0 +1,28 @@
//===-- Single-precision general exp/log functions ------------------------===//
//
// 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 "inv_trigf_utils.h"
namespace __llvm_libc {
// N[Table[ArcTan[x], {x, 1/16, 16/16, 1/16}], 40]
alignas(64) const double ATAN_T[ATAN_T_SIZE] = {
0x1.ff55bb72cfdeap-5, 0x1.fd5ba9aac2f6ep-4, 0x1.7b97b4bce5b02p-3,
0x1.f5b75f92c80ddp-3, 0x1.362773707ebccp-2, 0x1.6f61941e4def1p-2,
0x1.a64eec3cc23fdp-2, 0x1.dac670561bb4fp-2, 0x1.0657e94db30d0p-1,
0x1.1e00babdefeb4p-1, 0x1.345f01cce37bbp-1, 0x1.4978fa3269ee1p-1,
0x1.5d58987169b18p-1, 0x1.700a7c5784634p-1, 0x1.819d0b7158a4dp-1,
0x1.921fb54442d18p-1};
// for(int i = 0; i < 5; i++)
// printf("%.13a,\n", (-2 * (i % 2) + 1) * 1.0 / (2 * i + 1));
alignas(64) const double ATAN_K[5] = {
0x1.0000000000000p+0, -0x1.5555555555555p-2, 0x1.999999999999ap-3,
-0x1.2492492492492p-3, 0x1.c71c71c71c71cp-4};
} // namespace __llvm_libc

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@ -0,0 +1,94 @@
//===-- Single-precision general inverse trigonometric functions ----------===//
//
// 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_GENERIC_INV_TRIGF_UTILS_H
#define LLVM_LIBC_SRC_MATH_GENERIC_INV_TRIGF_UTILS_H
#include "math_utils.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/nearest_integer.h"
#include "src/__support/common.h"
#include <src/__support/FPUtil/NearestIntegerOperations.h>
#include <errno.h>
namespace __llvm_libc {
// PI / 2
constexpr double M_MATH_PI_2 = 0x1.921fb54442d18p+0;
// atan table size
constexpr int ATAN_T_BITS = 4;
constexpr int ATAN_T_SIZE = 1 << ATAN_T_BITS;
// N[Table[ArcTan[x], {x, 1/8, 8/8, 1/8}], 40]
extern const double ATAN_T[ATAN_T_SIZE];
extern const double ATAN_K[5];
// The main idea of the function is to use formula
// atan(u) + atan(v) = atan((u+v)/(1-uv))
// x should be positive, normal finite value
inline static double atan_eval(double x) {
using FPB = fputil::FPBits<double>;
// Added some small value to umin and umax mantissa to avoid possible rounding
// errors.
FPB::UIntType umin =
FPB::create_value(false, FPB::EXPONENT_BIAS - ATAN_T_BITS - 1,
0x100000000000UL)
.uintval();
FPB::UIntType umax =
FPB::create_value(false, FPB::EXPONENT_BIAS + ATAN_T_BITS,
0xF000000000000UL)
.uintval();
FPB bs(x);
bool sign = bs.get_sign();
auto x_abs = bs.uintval() & FPB::FloatProp::EXP_MANT_MASK;
if (x_abs <= umin) {
double pe = __llvm_libc::fputil::polyeval(x * x, 0.0, ATAN_K[1], ATAN_K[2],
ATAN_K[3], ATAN_K[4]);
return fputil::multiply_add(pe, x, x);
}
if (x_abs >= umax) {
double one_over_x_m = -1.0 / x;
double one_over_x2 = one_over_x_m * one_over_x_m;
double pe = __llvm_libc::fputil::polyeval(one_over_x2, ATAN_K[0], ATAN_K[1],
ATAN_K[2], ATAN_K[3]);
return fputil::multiply_add(pe, one_over_x_m, sign ? (-M_MATH_PI_2) : (M_MATH_PI_2));
}
double pos_x = FPB(x_abs).get_val();
bool one_over_x = pos_x > 1.0;
if (one_over_x) {
pos_x = 1.0 / pos_x;
}
double near_x = fputil::nearest_integer(pos_x * ATAN_T_SIZE);
int val = static_cast<int>(near_x);
near_x *= 1.0 / ATAN_T_SIZE;
double v = (pos_x - near_x) / fputil::multiply_add(near_x, pos_x, 1.0);
double v2 = v * v;
double pe = __llvm_libc::fputil::polyeval(v2, ATAN_K[0], ATAN_K[1], ATAN_K[2],
ATAN_K[3], ATAN_K[4]);
double result;
if (one_over_x)
result = M_PI_2 - fputil::multiply_add(pe, v, ATAN_T[val - 1]);
else
result = fputil::multiply_add(pe, v, ATAN_T[val - 1]);
return sign ? -result : result;
}
} // namespace __llvm_libc
#endif // LLVM_LIBC_SRC_MATH_GENERIC_INV_TRIGF_UTILS_H

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@ -1388,6 +1388,32 @@ add_fp_unittest(
libc.src.__support.FPUtil.fputil libc.src.__support.FPUtil.fputil
) )
add_fp_unittest(
atanf_test
NEED_MPFR
SUITE
libc_math_unittests
SRCS
atanf_test.cpp
DEPENDS
libc.src.math.atanf
libc.src.__support.FPUtil.fputil
)
add_fp_unittest(
inv_trigf_utils_test
NEED_MPFR
SUITE
libc_math_unittests
HDRS
in_float_range_test_helper.h
SRCS
inv_trigf_utils_test.cpp
DEPENDS
libc.src.math.generic.inv_trigf_utils
libc.src.__support.FPUtil.fputil
)
add_subdirectory(generic) add_subdirectory(generic)
add_subdirectory(exhaustive) add_subdirectory(exhaustive)
add_subdirectory(differential_testing) add_subdirectory(differential_testing)

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@ -0,0 +1,65 @@
//===-- Unittests for atanf -----------------------------------------------===//
//
// 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/atanf.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>
#include <initializer_list>
using FPBits = __llvm_libc::fputil::FPBits<float>;
namespace mpfr = __llvm_libc::testing::mpfr;
DECLARE_SPECIAL_CONSTANTS(float)
TEST(LlvmLibcAtanfTest, SpecialNumbers) {
errno = 0;
__llvm_libc::fputil::clear_except(FE_ALL_EXCEPT);
EXPECT_FP_EQ(aNaN, __llvm_libc::atanf(aNaN));
EXPECT_FP_EXCEPTION(FE_INVALID);
EXPECT_MATH_ERRNO(0);
__llvm_libc::fputil::clear_except(FE_ALL_EXCEPT);
EXPECT_FP_EQ(0.0f, __llvm_libc::atanf(0.0f));
EXPECT_FP_EXCEPTION(0);
EXPECT_MATH_ERRNO(0);
__llvm_libc::fputil::clear_except(FE_ALL_EXCEPT);
EXPECT_FP_EQ(-0.0f, __llvm_libc::atanf(-0.0f));
EXPECT_FP_EXCEPTION(0);
EXPECT_MATH_ERRNO(0);
}
TEST(LlvmLibcAtanfTest, InFloatRange) {
constexpr uint32_t COUNT = 1000000;
const uint32_t STEP = FPBits(inf).uintval() / COUNT;
for (uint32_t i = 0, v = 0; i <= COUNT; ++i, v += STEP) {
float x = float(FPBits(v));
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Atan, x,
__llvm_libc::atanf(x), 0.5);
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Atan, -x,
__llvm_libc::atanf(-x), 0.5);
}
}
// For small values, tanh(x) is x.
TEST(LlvmLibcAtanfTest, SpecialValues) {
for (uint32_t v : {0x3d8d6b23U, 0x3feefcfbU, 0xbd8d6b23U, 0xbfeefcfbU,
0x7F800000U, 0xFF800000U}) {
float x = float(FPBits(v));
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Atan, x,
__llvm_libc::atanf(x), 0.5);
}
}

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@ -307,3 +307,21 @@ add_fp_unittest(
LINK_LIBRARIES LINK_LIBRARIES
-lpthread -lpthread
) )
add_fp_unittest(
atanf_test
NO_RUN_POSTBUILD
NEED_MPFR
SUITE
libc_math_exhaustive_tests
SRCS
atanf_test.cpp
DEPENDS
.exhaustive_test
libc.include.math
libc.src.math.atanf
libc.src.__support.FPUtil.fputil
LINK_LIBRARIES
-lpthread
)

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@ -0,0 +1,76 @@
//===-- Exhaustive test for atanf -----------------------------------------===//
//
// 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/atanf.h"
#include "utils/MPFRWrapper/MPFRUtils.h"
#include <thread>
using FPBits = __llvm_libc::fputil::FPBits<float>;
namespace mpfr = __llvm_libc::testing::mpfr;
struct LlvmLibcAtanfExhaustiveTest : 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::Atan, x,
__llvm_libc::atanf(x), 0.5, rounding);
} while (bits++ < stop);
return result;
}
};
static const int NUM_THREADS = std::thread::hardware_concurrency();
// Range: [0, 1.0];
static const uint32_t POS_START = 0x0000'0000U;
static const uint32_t POS_STOP = FPBits::inf().uintval();
TEST_F(LlvmLibcAtanfExhaustiveTest, PostiveRangeRoundNearestTieToEven) {
test_full_range(POS_START, POS_STOP, mpfr::RoundingMode::Nearest);
}
TEST_F(LlvmLibcAtanfExhaustiveTest, PostiveRangeRoundUp) {
test_full_range(POS_START, POS_STOP, mpfr::RoundingMode::Upward);
}
TEST_F(LlvmLibcAtanfExhaustiveTest, PostiveRangeRoundDown) {
test_full_range(POS_START, POS_STOP, mpfr::RoundingMode::Downward);
}
TEST_F(LlvmLibcAtanfExhaustiveTest, PostiveRangeRoundTowardZero) {
test_full_range(POS_START, POS_STOP, mpfr::RoundingMode::TowardZero);
}
// Range: [-1.0, 0];
static const uint32_t NEG_START = 0x8000'0000U;
static const uint32_t NEG_STOP = FPBits::neg_inf().uintval();
TEST_F(LlvmLibcAtanfExhaustiveTest, NegativeRangeRoundNearestTieToEven) {
test_full_range(NEG_START, NEG_STOP, mpfr::RoundingMode::Nearest);
}
TEST_F(LlvmLibcAtanfExhaustiveTest, NegativeRangeRoundUp) {
test_full_range(NEG_START, NEG_STOP, mpfr::RoundingMode::Upward);
}
TEST_F(LlvmLibcAtanfExhaustiveTest, NegativeRangeRoundDown) {
test_full_range(NEG_START, NEG_STOP, mpfr::RoundingMode::Downward);
}
TEST_F(LlvmLibcAtanfExhaustiveTest, NegativeRangeRoundTowardZero) {
test_full_range(NEG_START, NEG_STOP, mpfr::RoundingMode::TowardZero);
}

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@ -1,4 +1,4 @@
//===-- Unittests for explogxf --------------------------------------------===// //===-- Unittests for supfuncf --------------------------------------------===//
// //
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information. // See https://llvm.org/LICENSE.txt for license information.

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@ -0,0 +1,32 @@
//===-- Unittests for supfuncf --------------------------------------------===//
//
// 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 "in_float_range_test_helper.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/math/generic/inv_trigf_utils.h"
#include "utils/MPFRWrapper/MPFRUtils.h"
#include "utils/UnitTest/FPMatcher.h"
#include "utils/UnitTest/Test.h"
#include <math.h>
namespace mpfr = __llvm_libc::testing::mpfr;
DECLARE_SPECIAL_CONSTANTS(float)
constexpr int def_count = 100003;
constexpr float def_prec = 0.500001f;
TEST(LlvmLibcAtanfPosTest, InFloatRange) {
CHECK_DATA(0.0f, inf, mpfr::Operation::Atan, __llvm_libc::atan_eval, isfinite,
def_count, def_prec);
}
TEST(LlvmLibcAtanfNegTest, InFloatRange) {
CHECK_DATA(-0.0f, neg_inf, mpfr::Operation::Atan, __llvm_libc::atan_eval,
isfinite, def_count, def_prec);
}

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@ -182,6 +182,12 @@ public:
return result; return result;
} }
MPFRNumber atan() const {
MPFRNumber result(*this);
mpfr_atan(result.value, value, mpfr_rounding);
return result;
}
MPFRNumber atanh() const { MPFRNumber atanh() const {
MPFRNumber result(*this); MPFRNumber result(*this);
mpfr_atanh(result.value, value, mpfr_rounding); mpfr_atanh(result.value, value, mpfr_rounding);
@ -506,6 +512,8 @@ unary_operation(Operation op, InputType input, unsigned int precision,
switch (op) { switch (op) {
case Operation::Abs: case Operation::Abs:
return mpfrInput.abs(); return mpfrInput.abs();
case Operation::Atan:
return mpfrInput.atan();
case Operation::Atanh: case Operation::Atanh:
return mpfrInput.atanh(); return mpfrInput.atanh();
case Operation::Ceil: case Operation::Ceil:

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@ -25,6 +25,7 @@ enum class Operation : int {
// and output floating point numbers are of the same kind. // and output floating point numbers are of the same kind.
BeginUnaryOperationsSingleOutput, BeginUnaryOperationsSingleOutput,
Abs, Abs,
Atan,
Atanh, Atanh,
Ceil, Ceil,
Cos, Cos,