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[libc][math] Refactor cos implementation to header-only in src/__support/math folder. (#151883)
Part of #147386 in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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-278
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16 files changed

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lines changed

‎libc/shared/math.h‎

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@@ -32,6 +32,7 @@
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#include "math/atanhf16.h"
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#include "math/cbrt.h"
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#include "math/cbrtf.h"
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#include "math/cos.h"
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#include "math/erff.h"
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#include "math/exp.h"
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#include "math/exp10.h"

‎libc/shared/math/cos.h‎

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//===-- Shared cos function -------------------------------------*- C++ -*-===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#ifndef LLVM_LIBC_SHARED_MATH_COS_H
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#define LLVM_LIBC_SHARED_MATH_COS_H
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#include "shared/libc_common.h"
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#include "src/__support/math/cos.h"
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namespace LIBC_NAMESPACE_DECL {
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namespace shared {
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using math::cos;
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} // namespace shared
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} // namespace LIBC_NAMESPACE_DECL
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#endif // LLVM_LIBC_SHARED_MATH_COS_H

‎libc/src/__support/math/CMakeLists.txt‎

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@@ -357,6 +357,24 @@ add_header_library(
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libc.src.__support.macros.optimization
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)
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add_header_library(
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cos
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HDRS
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cos.h
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DEPENDS
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libc.hdr.errno_macros
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libc.src.errno.errno
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libc.src.__support.FPUtil.double_double
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libc.src.__support.FPUtil.dyadic_float
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libc.src.__support.FPUtil.except_value_utils
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libc.src.__support.FPUtil.fenv_impl
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libc.src.__support.FPUtil.fp_bits
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libc.src.__support.math.range_reduction_double
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libc.src.__support.math.sincos_eval
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libc.src.__support.macros.optimization
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)
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add_header_library(
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erff
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HDRS
@@ -613,3 +631,32 @@ add_header_library(
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libc.src.__support.macros.optimization
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libc.src.__support.macros.properties.cpu_features
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)
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add_header_library(
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range_reduction_double
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HDRS
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range_reduction_double_common.h
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range_reduction_double_fma.h
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range_reduction_double_nofma.h
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DEPENDS
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libc.src.__support.FPUtil.double_double
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libc.src.__support.FPUtil.dyadic_float
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libc.src.__support.FPUtil.fp_bits
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libc.src.__support.FPUtil.fma
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libc.src.__support.FPUtil.multiply_add
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libc.src.__support.FPUtil.nearest_integer
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libc.src.__support.common
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libc.src.__support.integer_literals
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)
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add_header_library(
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sincos_eval
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HDRS
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sincos_eval.h
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DEPENDS
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libc.src.__support.FPUtil.double_double
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libc.src.__support.FPUtil.dyadic_float
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libc.src.__support.FPUtil.multiply_add
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libc.src.__support.FPUtil.polyeval
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libc.src.__support.integer_literals
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)

‎libc/src/__support/math/cos.h‎

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//===-- Implementation header for cos ---------------------------*- C++ -*-===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#ifndef LIBC_SRC___SUPPORT_MATH_COS_H
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#define LIBC_SRC___SUPPORT_MATH_COS_H
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#include "range_reduction_double_common.h"
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#include "sincos_eval.h"
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#include "src/__support/FPUtil/FEnvImpl.h"
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#include "src/__support/FPUtil/FPBits.h"
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#include "src/__support/FPUtil/double_double.h"
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#include "src/__support/FPUtil/dyadic_float.h"
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#include "src/__support/FPUtil/except_value_utils.h"
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#include "src/__support/macros/config.h"
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#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
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#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
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#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
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#include "range_reduction_double_fma.h"
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#else
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#include "range_reduction_double_nofma.h"
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#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
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namespace LIBC_NAMESPACE_DECL {
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namespace math {
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LIBC_INLINE static constexpr double cos(double x) {
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using namespace range_reduction_double_internal;
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using DoubleDouble = fputil::DoubleDouble;
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using FPBits = typename fputil::FPBits<double>;
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FPBits xbits(x);
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uint16_t x_e = xbits.get_biased_exponent();
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DoubleDouble y;
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unsigned k = 0;
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LargeRangeReduction range_reduction_large;
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// |x| < 2^16.
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if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT)) {
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// |x| < 2^-7
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if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 7)) {
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// |x| < 2^-27
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if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 27)) {
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// Signed zeros.
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if (LIBC_UNLIKELY(x == 0.0))
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return 1.0;
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// For |x| < 2^-27, |cos(x) - 1| < |x|^2/2 < 2^-54 = ulp(1 - 2^-53)/2.
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return fputil::round_result_slightly_down(1.0);
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}
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// No range reduction needed.
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k = 0;
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y.lo = 0.0;
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y.hi = x;
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} else {
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// Small range reduction.
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k = range_reduction_small(x, y);
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}
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} else {
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// Inf or NaN
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if (LIBC_UNLIKELY(x_e > 2 * FPBits::EXP_BIAS)) {
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if (xbits.is_signaling_nan()) {
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fputil::raise_except_if_required(FE_INVALID);
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return FPBits::quiet_nan().get_val();
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}
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// cos(+-Inf) = NaN
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if (xbits.get_mantissa() == 0) {
75+
fputil::set_errno_if_required(EDOM);
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fputil::raise_except_if_required(FE_INVALID);
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}
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return x + FPBits::quiet_nan().get_val();
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}
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// Large range reduction.
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k = range_reduction_large.fast(x, y);
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}
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DoubleDouble sin_y, cos_y;
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[[maybe_unused]] double err =
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math::sincos_eval_internal::sincos_eval(y, sin_y, cos_y);
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// Look up sin(k * pi/128) and cos(k * pi/128)
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#ifdef LIBC_MATH_HAS_SMALL_TABLES
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// Memory saving versions. Use 65-entry table.
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auto get_idx_dd = [](unsigned kk) -> DoubleDouble {
94+
unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
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DoubleDouble ans = SIN_K_PI_OVER_128[idx];
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if (kk & 128) {
97+
ans.hi = -ans.hi;
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ans.lo = -ans.lo;
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}
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return ans;
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};
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DoubleDouble msin_k = get_idx_dd(k + 128);
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DoubleDouble cos_k = get_idx_dd(k + 64);
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#else
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// Fast look up version, but needs 256-entry table.
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// -sin(k * pi/128) = sin((k + 128) * pi/128)
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// cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
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DoubleDouble msin_k = SIN_K_PI_OVER_128[(k + 128) & 255];
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DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 255];
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#endif // LIBC_MATH_HAS_SMALL_TABLES
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// After range reduction, k = round(x * 128 / pi) and y = x - k * (pi / 128).
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// So k is an integer and -pi / 256 <= y <= pi / 256.
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// Then cos(x) = cos((k * pi/128 + y)
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// = cos(y) * cos(k*pi/128) - sin(y) * sin(k*pi/128)
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DoubleDouble cos_k_cos_y = fputil::quick_mult(cos_y, cos_k);
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DoubleDouble msin_k_sin_y = fputil::quick_mult(sin_y, msin_k);
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DoubleDouble rr = fputil::exact_add<false>(cos_k_cos_y.hi, msin_k_sin_y.hi);
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rr.lo += msin_k_sin_y.lo + cos_k_cos_y.lo;
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#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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return rr.hi + rr.lo;
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#else
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using Float128 = typename fputil::DyadicFloat<128>;
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double rlp = rr.lo + err;
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double rlm = rr.lo - err;
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double r_upper = rr.hi + rlp; // (rr.lo + ERR);
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double r_lower = rr.hi + rlm; // (rr.lo - ERR);
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// Ziv's rounding test.
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if (LIBC_LIKELY(r_upper == r_lower))
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return r_upper;
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Float128 u_f128, sin_u, cos_u;
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if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT))
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u_f128 = range_reduction_small_f128(x);
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else
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u_f128 = range_reduction_large.accurate();
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math::sincos_eval_internal::sincos_eval(u_f128, sin_u, cos_u);
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auto get_sin_k = [](unsigned kk) -> Float128 {
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unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
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Float128 ans = SIN_K_PI_OVER_128_F128[idx];
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if (kk & 128)
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ans.sign = Sign::NEG;
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return ans;
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};
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// -sin(k * pi/128) = sin((k + 128) * pi/128)
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// cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
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Float128 msin_k_f128 = get_sin_k(k + 128);
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Float128 cos_k_f128 = get_sin_k(k + 64);
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// cos(x) = cos((k * pi/128 + u)
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// = cos(u) * cos(k*pi/128) - sin(u) * sin(k*pi/128)
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Float128 r = fputil::quick_add(fputil::quick_mul(cos_k_f128, cos_u),
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fputil::quick_mul(msin_k_f128, sin_u));
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// TODO: Add assertion if Ziv's accuracy tests fail in debug mode.
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// https://github.com/llvm/llvm-project/issues/96452.
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return static_cast<double>(r);
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#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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}
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} // namespace math
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} // namespace LIBC_NAMESPACE_DECL
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#endif // LIBC_SRC___SUPPORT_MATH_COS_H

‎libc/src/math/generic/range_reduction_double_common.h‎ renamed to ‎libc/src/__support/math/range_reduction_double_common.h‎

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//
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//===----------------------------------------------------------------------===//
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9-
#ifndef LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_DOUBLE_COMMON_H
10-
#define LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_DOUBLE_COMMON_H
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#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_RANGE_REDUCTION_DOUBLE_COMMON_H
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#define LLVM_LIBC_SRC___SUPPORT_MATH_RANGE_REDUCTION_DOUBLE_COMMON_H
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#include "src/__support/FPUtil/double_double.h"
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#include "src/__support/FPUtil/dyadic_float.h"
@@ -20,6 +20,10 @@
2020

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namespace LIBC_NAMESPACE_DECL {
2222

23+
namespace math {
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namespace range_reduction_double_internal {
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2327
#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
2428
static constexpr unsigned SPLIT = fputil::DefaultSplit<double>::VALUE;
2529
#else
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4044
// Error bound:
4145
// |(x - k * pi/128) - (u_hi + u_lo)| <= max(ulp(ulp(u_hi)), 2^-119)
4246
// <= 2^-111.
43-
LIBC_INLINE unsigned range_reduction_small(double x, DoubleDouble &u) {
47+
LIBC_INLINE static unsigned range_reduction_small(double x, DoubleDouble &u) {
4448
// Values of -pi/128 used for inputs with absolute value <= 2^16.
4549
// The first 3 parts are generated with (53 - 21 = 32)-bit precision, so that
4650
// the product k * MPI_OVER_128[i] is exact.
@@ -267,13 +271,15 @@ struct LargeRangeReduction {
267271
}
268272
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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274+
LIBC_INLINE LargeRangeReduction() = default;
275+
270276
private:
271277
// Index of x in the look-up table ONE_TWENTY_EIGHT_OVER_PI.
272-
unsigned idx;
278+
unsigned idx = 0;
273279
// x scaled down by 2^(-16 *(idx - 3))).
274-
double x_reduced;
280+
double x_reduced = 0;
275281
// Parts of (x * 128/pi) mod 1.
276-
double y_hi, y_lo;
282+
double y_hi = 0, y_lo = 0;
277283
DoubleDouble y_mid;
278284
};
279285

@@ -369,6 +375,10 @@ static constexpr Float128 SIN_K_PI_OVER_128_F128[65] = {
369375
};
370376
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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378+
} // namespace range_reduction_double_internal
379+
380+
} // namespace math
381+
372382
} // namespace LIBC_NAMESPACE_DECL
373383

374-
#endif // LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_DOUBLE_COMMON_H
384+
#endif // LLVM_LIBC_SRC___SUPPORT_MATH_RANGE_REDUCTION_DOUBLE_COMMON_H

‎libc/src/math/generic/range_reduction_double_fma.h‎ renamed to ‎libc/src/__support/math/range_reduction_double_fma.h‎

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66
//
77
//===----------------------------------------------------------------------===//
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#ifndef LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_DOUBLE_FMA_H
10-
#define LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_DOUBLE_FMA_H
9+
#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_RANGE_REDUCTION_DOUBLE_FMA_H
10+
#define LLVM_LIBC_SRC___SUPPORT_MATH_RANGE_REDUCTION_DOUBLE_FMA_H
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1212
#include "src/__support/FPUtil/FPBits.h"
1313
#include "src/__support/FPUtil/double_double.h"
1414
#include "src/__support/FPUtil/multiply_add.h"
1515
#include "src/__support/FPUtil/nearest_integer.h"
16-
#include "src/__support/common.h"
1716
#include "src/__support/macros/config.h"
18-
#include "src/__support/macros/optimization.h"
19-
#include "src/math/generic/range_reduction_double_common.h"
17+
#include "src/__support/math/range_reduction_double_common.h"
2018

2119
namespace LIBC_NAMESPACE_DECL {
2220

21+
namespace math {
22+
23+
namespace range_reduction_double_internal {
24+
2325
using LIBC_NAMESPACE::fputil::DoubleDouble;
2426

2527
LIBC_INLINE unsigned LargeRangeReduction::fast(double x, DoubleDouble &u) {
@@ -341,6 +343,10 @@ LIBC_INLINE constexpr DoubleDouble SIN_K_PI_OVER_128[] = {
341343
#endif // !LIBC_MATH_HAS_SMALL_TABLES
342344
};
343345

346+
} // namespace range_reduction_double_internal
347+
348+
} // namespace math
349+
344350
} // namespace LIBC_NAMESPACE_DECL
345351

346-
#endif // LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_DOUBLE_FMA_H
352+
#endif // LLVM_LIBC_SRC___SUPPORT_MATH_RANGE_REDUCTION_DOUBLE_FMA_H

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