[libc-commits] [libc] [libc][math] Implement double precision acos correctly rounded for all rounding modes. (PR #138308)
via libc-commits
libc-commits at lists.llvm.org
Fri May 2 11:30:10 PDT 2025
https://github.com/lntue updated https://github.com/llvm/llvm-project/pull/138308
>From 75e4c19fbbc60b54613c1b222cec07e7c8f16582 Mon Sep 17 00:00:00 2001
From: Tue Ly <lntue at google.com>
Date: Fri, 2 May 2025 12:48:18 -0400
Subject: [PATCH 1/2] [libc][math] Implement double precision acos correctly
rounded for all rounding modes.
---
libc/config/darwin/arm/entrypoints.txt | 1 +
libc/config/linux/aarch64/entrypoints.txt | 1 +
libc/config/linux/arm/entrypoints.txt | 1 +
libc/config/linux/riscv/entrypoints.txt | 1 +
libc/config/linux/x86_64/entrypoints.txt | 1 +
libc/config/windows/entrypoints.txt | 1 +
libc/docs/headers/math/index.rst | 2 +-
libc/src/math/generic/CMakeLists.txt | 21 ++
libc/src/math/generic/acos.cpp | 278 ++++++++++++++++++++++
libc/src/math/generic/asin_utils.h | 5 +
libc/test/src/math/CMakeLists.txt | 11 +
libc/test/src/math/acos_test.cpp | 82 +++++++
libc/test/src/math/smoke/CMakeLists.txt | 10 +
libc/test/src/math/smoke/acos_test.cpp | 53 +++++
14 files changed, 467 insertions(+), 1 deletion(-)
create mode 100644 libc/src/math/generic/acos.cpp
create mode 100644 libc/test/src/math/acos_test.cpp
create mode 100644 libc/test/src/math/smoke/acos_test.cpp
diff --git a/libc/config/darwin/arm/entrypoints.txt b/libc/config/darwin/arm/entrypoints.txt
index 70c888aec064c..308fc49d681d7 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.fenv.feupdateenv
# math.h entrypoints
+ libc.src.math.acos
libc.src.math.acosf
libc.src.math.acoshf
libc.src.math.asin
diff --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
index 66d7576ffb882..520046f768b5d 100644
--- a/libc/config/linux/aarch64/entrypoints.txt
+++ b/libc/config/linux/aarch64/entrypoints.txt
@@ -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
diff --git a/libc/config/linux/arm/entrypoints.txt b/libc/config/linux/arm/entrypoints.txt
index b5e2f59d25a54..7432a7e912e81 100644
--- a/libc/config/linux/arm/entrypoints.txt
+++ b/libc/config/linux/arm/entrypoints.txt
@@ -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
diff --git a/libc/config/linux/riscv/entrypoints.txt b/libc/config/linux/riscv/entrypoints.txt
index f2f895117e35a..987790c10bb6e 100644
--- a/libc/config/linux/riscv/entrypoints.txt
+++ b/libc/config/linux/riscv/entrypoints.txt
@@ -396,6 +396,7 @@ 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
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index 2ac016f065b2e..9f447dd0d35d2 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -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
diff --git a/libc/config/windows/entrypoints.txt b/libc/config/windows/entrypoints.txt
index 37fa888d6498a..09021a08cf731 100644
--- a/libc/config/windows/entrypoints.txt
+++ b/libc/config/windows/entrypoints.txt
@@ -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
diff --git a/libc/docs/headers/math/index.rst b/libc/docs/headers/math/index.rst
index 9d4d6698b6122..6b0365f481a4c 100644
--- a/libc/docs/headers/math/index.rst
+++ b/libc/docs/headers/math/index.rst
@@ -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 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index b08486ac61366..e5d1f9075bcb1 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -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
diff --git a/libc/src/math/generic/acos.cpp b/libc/src/math/generic/acos.cpp
new file mode 100644
index 0000000000000..a77ae10a344c7
--- /dev/null
+++ b/libc/src/math/generic/acos.cpp
@@ -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 PI_OVER_TWO.hi + (PI_OVER_TWO.lo + xbits.abs().get_val());
+#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 = x * 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, x_sign * PI.lo);
+ }
+ // |x| > 1, return NaN.
+ if (xbits.is_finite()) {
+ 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);
+ }
+ 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
diff --git a/libc/src/math/generic/asin_utils.h b/libc/src/math/generic/asin_utils.h
index 0bdf25367f820..1634525cce7ad 100644
--- a/libc/src/math/generic/asin_utils.h
+++ b/libc/src/math/generic/asin_utils.h
@@ -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};
@@ -548,6 +550,9 @@ 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],
diff --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt
index fba6b6f133163..9074524403102 100644
--- a/libc/test/src/math/CMakeLists.txt
+++ b/libc/test/src/math/CMakeLists.txt
@@ -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
diff --git a/libc/test/src/math/acos_test.cpp b/libc/test/src/math/acos_test.cpp
new file mode 100644
index 0000000000000..f2a18e7c60731
--- /dev/null
+++ b/libc/test/src/math/acos_test.cpp
@@ -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_nan() || FPBits(v).is_inf())
+ continue;
+ double result = LIBC_NAMESPACE::acos(x);
+ ++cc;
+ if (FPBits(result).is_nan() || FPBits(result).is_inf())
+ 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);
+}
diff --git a/libc/test/src/math/smoke/CMakeLists.txt b/libc/test/src/math/smoke/CMakeLists.txt
index ca1ce7fb1f48c..31f8aec5f310a 100644
--- a/libc/test/src/math/smoke/CMakeLists.txt
+++ b/libc/test/src/math/smoke/CMakeLists.txt
@@ -4051,6 +4051,16 @@ 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.src.math.acos
+)
+
add_fp_unittest(
acosf16_test
SUITE
diff --git a/libc/test/src/math/smoke/acos_test.cpp b/libc/test/src/math/smoke/acos_test.cpp
new file mode 100644
index 0000000000000..955b6e3e9ceb7
--- /dev/null
+++ b/libc/test/src/math/smoke/acos_test.cpp
@@ -0,0 +1,53 @@
+//===-- 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/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_ALL_ROUNDING(0x1.921fb54442d18p0, LIBC_NAMESPACE::acos(zero));
+ EXPECT_FP_EQ_ALL_ROUNDING(0x1.921fb54442d18p0,
+ LIBC_NAMESPACE::acos(neg_zero));
+ EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::acos(inf));
+ EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::acos(neg_inf));
+ EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::acos(2.0));
+ EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::acos(-2.0));
+ EXPECT_FP_EQ(zero, LIBC_NAMESPACE::acos(1.0));
+ EXPECT_FP_EQ(0x1.921fb54442d18p1, LIBC_NAMESPACE::acos(-1.0));
+}
+
+#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
>From efcc95b05a7010fbbb3d0596e1bd98a0158c0b9c Mon Sep 17 00:00:00 2001
From: Tue Ly <lntue at google.com>
Date: Fri, 2 May 2025 14:29:49 -0400
Subject: [PATCH 2/2] Fix close to 0 and close to -1 outputs.
---
libc/src/math/generic/acos.cpp | 5 ++---
libc/test/src/math/smoke/acos_test.cpp | 1 +
2 files changed, 3 insertions(+), 3 deletions(-)
diff --git a/libc/src/math/generic/acos.cpp b/libc/src/math/generic/acos.cpp
index a77ae10a344c7..9fc473ac1c334 100644
--- a/libc/src/math/generic/acos.cpp
+++ b/libc/src/math/generic/acos.cpp
@@ -40,7 +40,7 @@ LLVM_LIBC_FUNCTION(double, acos, (double x)) {
#else
// Force the evaluation and prevent constant propagation so that it
// is rounded correctly for FE_UPWARD rounding mode.
- return PI_OVER_TWO.hi + (PI_OVER_TWO.lo + xbits.abs().get_val());
+ return fputil::multiply_add(xbits.abs().get_val(), 0.75, PI_OVER_TWO.hi);
#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
}
@@ -118,8 +118,7 @@ LLVM_LIBC_FUNCTION(double, acos, (double x)) {
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, x_sign * PI.lo);
+ return x == 1.0 ? 0.0 : fputil::multiply_add(-x_sign, PI.hi, PI.lo);
}
// |x| > 1, return NaN.
if (xbits.is_finite()) {
diff --git a/libc/test/src/math/smoke/acos_test.cpp b/libc/test/src/math/smoke/acos_test.cpp
index 955b6e3e9ceb7..24fd685fa18ce 100644
--- a/libc/test/src/math/smoke/acos_test.cpp
+++ b/libc/test/src/math/smoke/acos_test.cpp
@@ -26,6 +26,7 @@ TEST_F(LlvmLibcAcosTest, SpecialNumbers) {
EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::acos(-2.0));
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
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