caio/clang-p2996
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

[libc][math] Implement double precision acos correctly rounded for all rounding modes. (#138308)

Browse Source 
We reduce computation of `acos` to `asin` as follow:

When `|x| < 0.5`:
```math
acos(x) = \frac{\pi}{2} - asin(x).
```
For `0.5 <= |x| < 1`, let
```math
u = \frac{1 - \left| x \right|}{2},
```
then
```math
acos(x) = \begin{cases}
  2 \cdot asin \left( \sqrt{u} \right) &, 0.5 \leq x < 1 \\
  \pi - 2 \cdot asin \left( \sqrt{u} \right) &, -1 < x \leq 0.5 
\end{cases}
```
This commit is contained in:
lntue
2025-05-08 21:23:09 -06:00
committed by GitHub
parent db2d5762eb
commit 78cc822aa6
16 changed files with 496 additions and 8 deletions
Download Patch File Download Diff File Expand all files Collapse all files

1
libc/config/darwin/arm/entrypoints.txt
View File

@@ -135,6 +135,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.fenv.feupdateenv
# math.h entrypoints
libc.src.math.acos
libc.src.math.acosf
libc.src.math.acoshf
libc.src.math.asin

1
libc/config/linux/aarch64/entrypoints.txt
View File

@@ -410,6 +410,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.fenv.feupdateenv
# math.h entrypoints
libc.src.math.acos
libc.src.math.acosf
libc.src.math.acoshf
libc.src.math.asin

1
libc/config/linux/arm/entrypoints.txt
View File

@@ -242,6 +242,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.fenv.feupdateenv
# math.h entrypoints
libc.src.math.acos
libc.src.math.acosf
libc.src.math.acoshf
libc.src.math.asin

1
libc/config/linux/riscv/entrypoints.txt
View File

@@ -416,6 +416,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.fenv.feupdateenv
# math.h entrypoints
libc.src.math.acos
libc.src.math.acosf
libc.src.math.acoshf
libc.src.math.asin

1
libc/config/linux/x86_64/entrypoints.txt
View File

@@ -415,6 +415,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.fenv.feupdateenv
# math.h entrypoints
libc.src.math.acos
libc.src.math.acosf
libc.src.math.acoshf
libc.src.math.asin

1
libc/config/windows/entrypoints.txt
View File

@@ -127,6 +127,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.fenv.feupdateenv
# math.h entrypoints
libc.src.math.acos
libc.src.math.acosf
libc.src.math.acoshf
libc.src.math.asin

2
libc/docs/headers/math/index.rst
View File

@@ -249,7 +249,7 @@ Higher Math Functions
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| <Func> | <Func_f> (float) | <Func> (double) | <Func_l> (long double) | <Func_f16> (float16) | <Func_f128> (float128) | C23 Definition Section | C23 Error Handling Section |
+===========+==================+=================+========================+======================+========================+========================+============================+
| acos | |check| | | | |check| | | 7.12.4.1 | F.10.1.1 |
| acos | |check| | |check| | | |check| | | 7.12.4.1 | F.10.1.1 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| acosh | |check| | | | |check| | | 7.12.5.1 | F.10.2.1 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

6
libc/include/math.yaml
View File

@@ -8,6 +8,12 @@ types:
enums: []
objects: []
functions:
- name: acos
standards:
- stdc
return_type: double
arguments:
- type: double
- name: acosf
standards:
- stdc

21
libc/src/math/generic/CMakeLists.txt
View File

@@ -4117,6 +4117,7 @@ add_entrypoint_object(
HDRS
../asin.h
DEPENDS
.asin_utils
libc.src.__support.FPUtil.double_double
libc.src.__support.FPUtil.dyadic_float
libc.src.__support.FPUtil.fenv_impl
@@ -4164,6 +4165,26 @@ add_entrypoint_object(
libc.src.__support.macros.properties.types
)
add_entrypoint_object(
acos
SRCS
acos.cpp
HDRS
../acos.h
DEPENDS
.asin_utils
libc.src.__support.FPUtil.double_double
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.polyeval
libc.src.__support.FPUtil.sqrt
libc.src.__support.macros.optimization
libc.src.__support.macros.properties.types
libc.src.__support.macros.properties.cpu_features
)
add_entrypoint_object(
acospif16
SRCS

278
libc/src/math/generic/acos.cpp Normal file
View File

@@ -0,0 +1,278 @@
//===-- Double-precision acos 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/acos.h"
#include "asin_utils.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/multiply_add.h"
#include "src/__support/FPUtil/sqrt.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
namespace LIBC_NAMESPACE_DECL {
using DoubleDouble = fputil::DoubleDouble;
using Float128 = fputil::DyadicFloat<128>;
LLVM_LIBC_FUNCTION(double, acos, (double x)) {
using FPBits = fputil::FPBits<double>;
FPBits xbits(x);
int x_exp = xbits.get_biased_exponent();
// |x| < 0.5.
if (x_exp < FPBits::EXP_BIAS - 1) {
// |x| < 2^-55.
if (LIBC_UNLIKELY(x_exp < FPBits::EXP_BIAS - 55)) {
// When |x| < 2^-55, acos(x) = pi/2
#if defined(LIBC_MATH_HAS_SKIP_ACCURATE_PASS)
return PI_OVER_TWO.hi;
#else
// Force the evaluation and prevent constant propagation so that it
// is rounded correctly for FE_UPWARD rounding mode.
return (xbits.abs().get_val() + 0x1.0p-160) + PI_OVER_TWO.hi;
#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
}
#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
// acos(x) = pi/2 - asin(x)
// = pi/2 - x * P(x^2)
double p = asin_eval(x * x);
return PI_OVER_TWO.hi + fputil::multiply_add(-x, p, PI_OVER_TWO.lo);
#else
unsigned idx;
DoubleDouble x_sq = fputil::exact_mult(x, x);
double err = xbits.abs().get_val() * 0x1.0p-51;
// Polynomial approximation:
// p ~ asin(x)/x
DoubleDouble p = asin_eval(x_sq, idx, err);
// asin(x) ~ x * p
DoubleDouble r0 = fputil::exact_mult(x, p.hi);
// acos(x) = pi/2 - asin(x)
// ~ pi/2 - x * p
// = pi/2 - x * (p.hi + p.lo)
double r_hi = fputil::multiply_add(-x, p.hi, PI_OVER_TWO.hi);
// Use Dekker's 2SUM algorithm to compute the lower part.
double r_lo = ((PI_OVER_TWO.hi - r_hi) - r0.hi) - r0.lo;
r_lo = fputil::multiply_add(-x, p.lo, r_lo + PI_OVER_TWO.lo);
// Ziv's accuracy test.
double r_upper = r_hi + (r_lo + err);
double r_lower = r_hi + (r_lo - err);
if (LIBC_LIKELY(r_upper == r_lower))
return r_upper;
// Ziv's accuracy test failed, perform 128-bit calculation.
// Recalculate mod 1/64.
idx = static_cast<unsigned>(fputil::nearest_integer(x_sq.hi * 0x1.0p6));
// Get x^2 - idx/64 exactly. When FMA is available, double-double
// multiplication will be correct for all rounding modes. Otherwise we use
// Float128 directly.
Float128 x_f128(x);
#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
// u = x^2 - idx/64
Float128 u_hi(
fputil::multiply_add(static_cast<double>(idx), -0x1.0p-6, x_sq.hi));
Float128 u = fputil::quick_add(u_hi, Float128(x_sq.lo));
#else
Float128 x_sq_f128 = fputil::quick_mul(x_f128, x_f128);
Float128 u = fputil::quick_add(
x_sq_f128, Float128(static_cast<double>(idx) * (-0x1.0p-6)));
#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
Float128 p_f128 = asin_eval(u, idx);
// Flip the sign of x_f128 to perform subtraction.
x_f128.sign = x_f128.sign.negate();
Float128 r =
fputil::quick_add(PI_OVER_TWO_F128, fputil::quick_mul(x_f128, p_f128));
return static_cast<double>(r);
#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
}
// |x| >= 0.5
double x_abs = xbits.abs().get_val();
// Maintaining the sign:
constexpr double SIGN[2] = {1.0, -1.0};
double x_sign = SIGN[xbits.is_neg()];
// |x| >= 1
if (LIBC_UNLIKELY(x_exp >= FPBits::EXP_BIAS)) {
// x = +-1, asin(x) = +- pi/2
if (x_abs == 1.0) {
// x = 1, acos(x) = 0,
// x = -1, acos(x) = pi
return x == 1.0 ? 0.0 : fputil::multiply_add(-x_sign, PI.hi, PI.lo);
}
// |x| > 1, return NaN.
if (xbits.is_quiet_nan())
return x;
// Set domain error for non-NaN input.
if (!xbits.is_nan())
fputil::set_errno_if_required(EDOM);
fputil::raise_except_if_required(FE_INVALID);
return FPBits::quiet_nan().get_val();
}
// When |x| >= 0.5, we perform range reduction as follow:
//
// When 0.5 <= x < 1, let:
// y = acos(x)
// We will use the double angle formula:
// cos(2y) = 1 - 2 sin^2(y)
// and the complement angle identity:
// 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 ) )
// Equivalently:
// acos(x) = 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 reduce to the previous case using the formula:
// acos(x) = pi - acos(-x)
// = pi - 2 * asin ( sqrt( (1 + x)/2 ) )
// ~ pi - 2 * sqrt(u) * P(u),
// where u = (1 - |x|)/2.
// u = (1 - |x|)/2
double u = fputil::multiply_add(x_abs, -0.5, 0.5);
// v_hi + v_lo ~ sqrt(u).
// Let:
// h = u - v_hi^2 = (sqrt(u) - v_hi) * (sqrt(u) + v_hi)
// Then:
// sqrt(u) = v_hi + h / (sqrt(u) + v_hi)
// ~ v_hi + h / (2 * v_hi)
// So we can use:
// v_lo = h / (2 * v_hi).
double v_hi = fputil::sqrt<double>(u);
#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
constexpr DoubleDouble CONST_TERM[2] = {{0.0, 0.0}, PI};
DoubleDouble const_term = CONST_TERM[xbits.is_neg()];
double p = asin_eval(u);
double scale = x_sign * 2.0 * v_hi;
double r = const_term.hi + fputil::multiply_add(scale, p, const_term.lo);
return r;
#else
#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
double h = fputil::multiply_add(v_hi, -v_hi, u);
#else
DoubleDouble v_hi_sq = fputil::exact_mult(v_hi, v_hi);
double h = (u - v_hi_sq.hi) - v_hi_sq.lo;
#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
// Scale v_lo and v_hi by 2 from the formula:
// vh = v_hi * 2
// vl = 2*v_lo = h / v_hi.
double vh = v_hi * 2.0;
double vl = h / v_hi;
// Polynomial approximation:
// p ~ asin(sqrt(u))/sqrt(u)
unsigned idx;
double err = vh * 0x1.0p-51;
DoubleDouble p = asin_eval(DoubleDouble{0.0, u}, idx, err);
// Perform computations in double-double arithmetic:
// asin(x) = pi/2 - (v_hi + v_lo) * (ASIN_COEFFS[idx][0] + p)
DoubleDouble r0 = fputil::quick_mult(DoubleDouble{vl, vh}, p);
double r_hi, r_lo;
if (xbits.is_pos()) {
r_hi = r0.hi;
r_lo = r0.lo;
} else {
DoubleDouble r = fputil::exact_add(PI.hi, -r0.hi);
r_hi = r.hi;
r_lo = (PI.lo - r0.lo) + r.lo;
}
// Ziv's accuracy test.
double r_upper = r_hi + (r_lo + err);
double r_lower = r_hi + (r_lo - err);
if (LIBC_LIKELY(r_upper == r_lower))
return r_upper;
// Ziv's accuracy test failed, we redo the computations in Float128.
// Recalculate mod 1/64.
idx = static_cast<unsigned>(fputil::nearest_integer(u * 0x1.0p6));
// After the first step of Newton-Raphson approximating v = sqrt(u), we have
// that:
// sqrt(u) = v_hi + h / (sqrt(u) + v_hi)
// v_lo = h / (2 * v_hi)
// With error:
// sqrt(u) - (v_hi + v_lo) = h * ( 1/(sqrt(u) + v_hi) - 1/(2*v_hi) )
// = -h^2 / (2*v * (sqrt(u) + v)^2).
// Since:
// (sqrt(u) + v_hi)^2 ~ (2sqrt(u))^2 = 4u,
// we can add another correction term to (v_hi + v_lo) that is:
// v_ll = -h^2 / (2*v_hi * 4u)
// = -v_lo * (h / 4u)
// = -vl * (h / 8u),
// making the errors:
// sqrt(u) - (v_hi + v_lo + v_ll) = O(h^3)
// well beyond 128-bit precision needed.
// Get the rounding error of vl = 2 * v_lo ~ h / vh
// Get full product of vh * vl
#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
double vl_lo = fputil::multiply_add(-v_hi, vl, h) / v_hi;
#else
DoubleDouble vh_vl = fputil::exact_mult(v_hi, vl);
double vl_lo = ((h - vh_vl.hi) - vh_vl.lo) / v_hi;
#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
// vll = 2*v_ll = -vl * (h / (4u)).
double t = h * (-0.25) / u;
double vll = fputil::multiply_add(vl, t, vl_lo);
// m_v = -(v_hi + v_lo + v_ll).
Float128 m_v = fputil::quick_add(
Float128(vh), fputil::quick_add(Float128(vl), Float128(vll)));
m_v.sign = xbits.sign();
// Perform computations in Float128:
// acos(x) = (v_hi + v_lo + vll) * P(u) , when 0.5 <= x < 1,
// = pi - (v_hi + v_lo + vll) * P(u) , when -1 < x <= -0.5.
Float128 y_f128(fputil::multiply_add(static_cast<double>(idx), -0x1.0p-6, u));
Float128 p_f128 = asin_eval(y_f128, idx);
Float128 r_f128 = fputil::quick_mul(m_v, p_f128);
if (xbits.is_neg())
r_f128 = fputil::quick_add(PI_F128, r_f128);
return static_cast<double>(r_f128);
#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
}
} // namespace LIBC_NAMESPACE_DECL

14
libc/src/math/generic/asin.cpp
View File

@@ -74,7 +74,7 @@ LLVM_LIBC_FUNCTION(double, asin, (double x)) {
#else
unsigned idx;
DoubleDouble x_sq = fputil::exact_mult(x, x);
double err = x * 0x1.0p-51;
double err = xbits.abs().get_val() * 0x1.0p-51;
// Polynomial approximation:
// p ~ asin(x)/x
@@ -135,12 +135,14 @@ LLVM_LIBC_FUNCTION(double, asin, (double x)) {
x_sign * PI_OVER_TWO.lo);
}
// |x| > 1, return NaN.
if (xbits.is_finite()) {
if (xbits.is_quiet_nan())
return x;
// Set domain error for non-NaN input.
if (!xbits.is_nan())
fputil::set_errno_if_required(EDOM);
fputil::raise_except_if_required(FE_INVALID);
} else if (xbits.is_signaling_nan()) {
fputil::raise_except_if_required(FE_INVALID);
}
fputil::raise_except_if_required(FE_INVALID);
return FPBits::quiet_nan().get_val();
}

8
libc/src/math/generic/asin_utils.h
View File

@@ -25,6 +25,8 @@ namespace {
using DoubleDouble = fputil::DoubleDouble;
using Float128 = fputil::DyadicFloat<128>;
constexpr DoubleDouble PI = {0x1.1a62633145c07p-53, 0x1.921fb54442d18p1};
constexpr DoubleDouble PI_OVER_TWO = {0x1.1a62633145c07p-54,
0x1.921fb54442d18p0};
@@ -172,7 +174,8 @@ LIBC_INLINE DoubleDouble asin_eval(const DoubleDouble &u, unsigned &idx,
double y_hi = multiply_add(k, -0x1.0p-5, u.hi); // Exact
DoubleDouble y = fputil::exact_add(y_hi, u.lo);
double y2 = y.hi * y.hi;
err *= y2 + 0x1.0p-30;
// Add double-double errors in addition to the relative errors from y2.
err = fputil::multiply_add(err, y2, 0x1.0p-102);
DoubleDouble c0 = fputil::quick_mult(
y, DoubleDouble{ASIN_COEFFS[idx][3], ASIN_COEFFS[idx][2]});
double c1 = multiply_add(y.hi, ASIN_COEFFS[idx][5], ASIN_COEFFS[idx][4]);
@@ -548,6 +551,9 @@ constexpr Float128 ASIN_COEFFS_F128[17][16] = {
constexpr Float128 PI_OVER_TWO_F128 = {
Sign::POS, -127, 0xc90fdaa2'2168c234'c4c6628b'80dc1cd1_u128};
constexpr Float128 PI_F128 = {Sign::POS, -126,
0xc90fdaa2'2168c234'c4c6628b'80dc1cd1_u128};
LIBC_INLINE Float128 asin_eval(const Float128 &u, unsigned idx) {
return fputil::polyeval(u, ASIN_COEFFS_F128[idx][0], ASIN_COEFFS_F128[idx][1],
ASIN_COEFFS_F128[idx][2], ASIN_COEFFS_F128[idx][3],

11
libc/test/src/math/CMakeLists.txt
View File

@@ -2280,6 +2280,17 @@ add_fp_unittest(
libc.src.__support.FPUtil.fp_bits
)
add_fp_unittest(
acos_test
NEED_MPFR
SUITE
libc-math-unittests
SRCS
acos_test.cpp
DEPENDS
libc.src.math.acos
)
add_fp_unittest(
acosf16_test
NEED_MPFR

82
libc/test/src/math/acos_test.cpp Normal file
View File

@@ -0,0 +1,82 @@
//===-- Unittests for acos ------------------------------------------------===//
//
// 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/acos.h"
#include "test/UnitTest/FPMatcher.h"
#include "test/UnitTest/Test.h"
#include "utils/MPFRWrapper/MPFRUtils.h"
using LlvmLibcAcosTest = LIBC_NAMESPACE::testing::FPTest<double>;
namespace mpfr = LIBC_NAMESPACE::testing::mpfr;
using LIBC_NAMESPACE::testing::tlog;
TEST_F(LlvmLibcAcosTest, InDoubleRange) {
constexpr uint64_t COUNT = 123'451;
uint64_t START = FPBits(0x1.0p-60).uintval();
uint64_t STOP = FPBits(1.0).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 = 0.0, 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 (FPBits(v).is_inf_or_nan())
continue;
double result = LIBC_NAMESPACE::acos(x);
++cc;
if (FPBits(result).is_inf_or_nan())
continue;
++count;
if (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Acos, x, result,
0.5, rounding_mode)) {
++fails;
while (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Acos, x,
result, tol, rounding_mode)) {
mx = x;
mr = result;
if (tol > 1000.0)
break;
tol *= 2.0;
}
}
}
if (fails) {
tlog << " Acos failed: " << fails << "/" << count << "/" << cc
<< " tests.\n";
tlog << " Max ULPs is at most: " << static_cast<uint64_t>(tol) << ".\n";
EXPECT_MPFR_MATCH(mpfr::Operation::Acos, 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);
}

12
libc/test/src/math/smoke/CMakeLists.txt
View File

@@ -4051,6 +4051,18 @@ add_fp_unittest(
libc.src.__support.FPUtil.fp_bits
)
add_fp_unittest(
acos_test
SUITE
libc-math-smoke-tests
SRCS
acos_test.cpp
DEPENDS
libc.hdr.fenv_macros
libc.src.errno.errno
libc.src.math.acos
)
add_fp_unittest(
acosf16_test
SUITE

64
libc/test/src/math/smoke/acos_test.cpp Normal file
View File

@@ -0,0 +1,64 @@
//===-- Unittests for acos ------------------------------------------------===//
//
// 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 "hdr/fenv_macros.h"
#include "src/errno/libc_errno.h"
#include "src/math/acos.h"
#include "test/UnitTest/FPMatcher.h"
#include "test/UnitTest/Test.h"
using LlvmLibcAcosTest = LIBC_NAMESPACE::testing::FPTest<double>;
TEST_F(LlvmLibcAcosTest, SpecialNumbers) {
EXPECT_FP_EQ_WITH_EXCEPTION_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::acos(sNaN),
FE_INVALID);
EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::acos(aNaN));
EXPECT_FP_EQ(0x1.921fb54442d18p0, LIBC_NAMESPACE::acos(zero));
EXPECT_FP_EQ(0x1.921fb54442d18p0, LIBC_NAMESPACE::acos(neg_zero));
LIBC_NAMESPACE::libc_errno = 0;
EXPECT_FP_EQ_WITH_EXCEPTION_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::acos(inf),
FE_INVALID);
EXPECT_MATH_ERRNO(EDOM);
EXPECT_FP_EQ_WITH_EXCEPTION_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::acos(neg_inf),
FE_INVALID);
EXPECT_MATH_ERRNO(EDOM);
EXPECT_FP_EQ_WITH_EXCEPTION_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::acos(2.0),
FE_INVALID);
EXPECT_MATH_ERRNO(EDOM);
EXPECT_FP_EQ_WITH_EXCEPTION_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::acos(-2.0),
FE_INVALID);
EXPECT_MATH_ERRNO(EDOM);
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::acos(1.0));
EXPECT_FP_EQ(0x1.921fb54442d18p1, LIBC_NAMESPACE::acos(-1.0));
EXPECT_FP_EQ(0x1.921fb54442d18p0, LIBC_NAMESPACE::acos(0x1.0p-54));
}
#ifdef LIBC_TEST_FTZ_DAZ
using namespace LIBC_NAMESPACE::testing;
TEST_F(LlvmLibcAcosTest, FTZMode) {
ModifyMXCSR mxcsr(FTZ);
EXPECT_FP_EQ(0x1.921fb54442d18p0, LIBC_NAMESPACE::acos(min_denormal));
}
TEST_F(LlvmLibcAcosTest, DAZMode) {
ModifyMXCSR mxcsr(DAZ);
EXPECT_FP_EQ(0x1.921fb54442d18p0, LIBC_NAMESPACE::acos(min_denormal));
}
TEST_F(LlvmLibcAcosTest, FTZDAZMode) {
ModifyMXCSR mxcsr(FTZ | DAZ);
EXPECT_FP_EQ(0x1.921fb54442d18p0, LIBC_NAMESPACE::acos(min_denormal));
}
#endif