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[libc][math] Refactor exp10f16 implementation to header-only in src/__support/math folder. (llvm#148408)
Part of llvm#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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-194
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‎libc/shared/math.h‎

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#include "math/exp.h"
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#include "math/exp10.h"
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#include "math/exp10f.h"
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#include "math/exp10f16.h"
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#include "math/expf.h"
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#include "math/expf16.h"
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#include "math/frexpf.h"

‎libc/shared/math/exp10f16.h‎

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//===-- Shared exp10f16 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_EXP10F_H
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#define LLVM_LIBC_SHARED_MATH_EXP10F_H
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#include "include/llvm-libc-macros/float16-macros.h"
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#ifdef LIBC_TYPES_HAS_FLOAT16
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#include "shared/libc_common.h"
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#include "src/__support/math/exp10f16.h"
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namespace LIBC_NAMESPACE_DECL {
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namespace shared {
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using math::exp10f16;
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} // namespace shared
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} // namespace LIBC_NAMESPACE_DECL
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#endif // LIBC_TYPES_HAS_FLOAT16
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#endif // LLVM_LIBC_SHARED_MATH_EXP10F_H

‎libc/src/__support/math/CMakeLists.txt‎

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@@ -198,3 +198,37 @@ add_header_library(
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libc.src.__support.FPUtil.rounding_mode
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libc.src.__support.macros.optimization
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)
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add_header_library(
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exp10_float16_constants
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HDRS
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exp10_float16_constants.h
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DEPENDS
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libc.src.__support.CPP.array
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)
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add_header_library(
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exp10f16_utils
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HDRS
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exp10f16_utils.h
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DEPENDS
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.expf16_utils
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.exp10_float16_constants
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libc.src.__support.FPUtil.fp_bits
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)
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add_header_library(
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exp10f16
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HDRS
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exp10f16.h
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DEPENDS
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.exp10f16_utils
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libc.src.__support.FPUtil.fp_bits
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src.__support.FPUtil.FEnvImpl
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src.__support.FPUtil.FPBits
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src.__support.FPUtil.cast
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src.__support.FPUtil.rounding_mode
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src.__support.FPUtil.except_value_utils
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src.__support.macros.optimization
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src.__support.macros.properties.cpu_features
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)

‎libc/src/__support/math/exp10_float16_constants.h‎

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//===-- Constants for exp10f16 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_SRC___SUPPORT_MATH_EXP10_FLOAT16_CONSTANTS_H
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#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP10_FLOAT16_CONSTANTS_H
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#include "include/llvm-libc-macros/float16-macros.h"
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#include <stdint.h>
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#ifdef LIBC_TYPES_HAS_FLOAT16
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#include "src/__support/CPP/array.h"
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namespace LIBC_NAMESPACE_DECL {
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// Generated by Sollya with the following commands:
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// > display = hexadecimal;
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// > for i from 0 to 7 do printsingle(round(2^(i * 2^-3), SG, RN));
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static constexpr cpp::array<uint32_t, 8> EXP2_MID_BITS = {
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0x3f80'0000U, 0x3f8b'95c2U, 0x3f98'37f0U, 0x3fa5'fed7U,
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0x3fb5'04f3U, 0x3fc5'672aU, 0x3fd7'44fdU, 0x3fea'c0c7U,
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};
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// Generated by Sollya with the following commands:
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// > display = hexadecimal;
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// > round(log2(10), SG, RN);
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static constexpr float LOG2F_10 = 0x1.a934fp+1f;
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// Generated by Sollya with the following commands:
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// > display = hexadecimal;
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// > round(log10(2), SG, RN);
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static constexpr float LOG10F_2 = 0x1.344136p-2f;
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} // namespace LIBC_NAMESPACE_DECL
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#endif // LIBC_TYPES_HAS_FLOAT16
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#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F16_H

‎libc/src/__support/math/exp10f16.h‎

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//===-- Implementation header for exp10f16 ----------------------*- 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_SRC___SUPPORT_MATH_EXP10F16_H
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#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F16_H
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#include "include/llvm-libc-macros/float16-macros.h"
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#ifdef LIBC_TYPES_HAS_FLOAT16
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#include "exp10f16_utils.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/cast.h"
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#include "src/__support/FPUtil/except_value_utils.h"
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#include "src/__support/FPUtil/rounding_mode.h"
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#include "src/__support/macros/config.h"
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#include "src/__support/macros/optimization.h"
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#include "src/__support/macros/properties/cpu_features.h"
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namespace LIBC_NAMESPACE_DECL {
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namespace math {
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#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT
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static constexpr size_t N_EXP10F16_EXCEPTS = 5;
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#else
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static constexpr size_t N_EXP10F16_EXCEPTS = 8;
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#endif
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static constexpr fputil::ExceptValues<float16, N_EXP10F16_EXCEPTS>
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EXP10F16_EXCEPTS = {{
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// x = 0x1.8f4p-2, exp10f16(x) = 0x1.3ap+1 (RZ)
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{0x363dU, 0x40e8U, 1U, 0U, 1U},
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// x = 0x1.95cp-2, exp10f16(x) = 0x1.3ecp+1 (RZ)
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{0x3657U, 0x40fbU, 1U, 0U, 0U},
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// x = -0x1.018p-4, exp10f16(x) = 0x1.bbp-1 (RZ)
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{0xac06U, 0x3aecU, 1U, 0U, 0U},
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// x = -0x1.c28p+0, exp10f16(x) = 0x1.1ccp-6 (RZ)
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{0xbf0aU, 0x2473U, 1U, 0U, 0U},
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// x = -0x1.e1cp+1, exp10f16(x) = 0x1.694p-13 (RZ)
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{0xc387U, 0x09a5U, 1U, 0U, 0U},
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#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
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// x = 0x1.0cp+1, exp10f16(x) = 0x1.f04p+6 (RZ)
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{0x4030U, 0x57c1U, 1U, 0U, 1U},
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// x = 0x1.1b8p+1, exp10f16(x) = 0x1.47cp+7 (RZ)
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{0x406eU, 0x591fU, 1U, 0U, 1U},
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// x = 0x1.1b8p+2, exp10f16(x) = 0x1.a4p+14 (RZ)
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{0x446eU, 0x7690U, 1U, 0U, 1U},
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#endif
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}};
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#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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static constexpr float16 exp10f16(float16 x) {
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using FPBits = fputil::FPBits<float16>;
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FPBits x_bits(x);
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uint16_t x_u = x_bits.uintval();
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uint16_t x_abs = x_u & 0x7fffU;
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// When |x| >= 5, or x is NaN.
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if (LIBC_UNLIKELY(x_abs >= 0x4500U)) {
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// exp10(NaN) = NaN
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if (x_bits.is_nan()) {
71+
if (x_bits.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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return x;
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}
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// When x >= 5.
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if (x_bits.is_pos()) {
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// exp10(+inf) = +inf
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if (x_bits.is_inf())
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return FPBits::inf().get_val();
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switch (fputil::quick_get_round()) {
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case FE_TONEAREST:
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case FE_UPWARD:
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fputil::set_errno_if_required(ERANGE);
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fputil::raise_except_if_required(FE_OVERFLOW);
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return FPBits::inf().get_val();
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default:
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return FPBits::max_normal().get_val();
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}
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}
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// When x <= -8.
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if (x_u >= 0xc800U) {
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// exp10(-inf) = +0
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if (x_bits.is_inf())
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return FPBits::zero().get_val();
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fputil::set_errno_if_required(ERANGE);
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fputil::raise_except_if_required(FE_UNDERFLOW | FE_INEXACT);
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if (fputil::fenv_is_round_up())
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return FPBits::min_subnormal().get_val();
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return FPBits::zero().get_val();
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}
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}
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// When x is 1, 2, 3, or 4. These are hard-to-round cases with exact results.
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if (LIBC_UNLIKELY((x_u & ~(0x3c00U | 0x4000U | 0x4200U | 0x4400U)) == 0)) {
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switch (x_u) {
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case 0x3c00U: // x = 1.0f16
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return fputil::cast<float16>(10.0);
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case 0x4000U: // x = 2.0f16
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return fputil::cast<float16>(100.0);
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case 0x4200U: // x = 3.0f16
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return fputil::cast<float16>(1'000.0);
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case 0x4400U: // x = 4.0f16
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return fputil::cast<float16>(10'000.0);
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}
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}
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#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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if (auto r = EXP10F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
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return r.value();
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#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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// 10^x = 2^((hi + mid) * log2(10)) * 10^lo
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auto [exp2_hi_mid, exp10_lo] = exp10_range_reduction(x);
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return fputil::cast<float16>(exp2_hi_mid * exp10_lo);
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}
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} // namespace math
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} // namespace LIBC_NAMESPACE_DECL
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#endif // LIBC_TYPES_HAS_FLOAT16
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#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F16_H

‎libc/src/__support/math/exp10f16_utils.h‎

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//===-- Common utils for exp10f16 -------------------------------*- 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_SRC___SUPPORT_MATH_EXP10F16_UTILS_H
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#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F16_UTILS_H
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#include "include/llvm-libc-macros/float16-macros.h"
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#ifdef LIBC_TYPES_HAS_FLOAT16
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#include "exp10_float16_constants.h"
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#include "expf16_utils.h"
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#include "src/__support/FPUtil/FPBits.h"
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namespace LIBC_NAMESPACE_DECL {
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LIBC_INLINE static constexpr ExpRangeReduction
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exp10_range_reduction(float16 x) {
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// For -8 < x < 5, to compute 10^x, we perform the following range reduction:
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// find hi, mid, lo, such that:
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// x = (hi + mid) * log2(10) + lo, in which
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// hi is an integer,
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// mid * 2^3 is an integer,
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// -2^(-4) <= lo < 2^(-4).
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// In particular,
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// hi + mid = round(x * 2^3) * 2^(-3).
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// Then,
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// 10^x = 10^(hi + mid + lo) = 2^((hi + mid) * log2(10)) + 10^lo
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// We store 2^mid in the lookup table EXP2_MID_BITS, and compute 2^hi * 2^mid
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// by adding hi to the exponent field of 2^mid. 10^lo is computed using a
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// degree-4 minimax polynomial generated by Sollya.
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float xf = x;
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float kf = fputil::nearest_integer(xf * (LOG2F_10 * 0x1.0p+3f));
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int x_hi_mid = static_cast<int>(kf);
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unsigned x_hi = static_cast<unsigned>(x_hi_mid) >> 3;
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unsigned x_mid = static_cast<unsigned>(x_hi_mid) & 0x7;
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// lo = x - (hi + mid) = round(x * 2^3 * log2(10)) * log10(2) * (-2^(-3)) + x
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float lo = fputil::multiply_add(kf, LOG10F_2 * -0x1.0p-3f, xf);
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uint32_t exp2_hi_mid_bits =
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EXP2_MID_BITS[x_mid] +
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static_cast<uint32_t>(x_hi << fputil::FPBits<float>::FRACTION_LEN);
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float exp2_hi_mid = fputil::FPBits<float>(exp2_hi_mid_bits).get_val();
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// Degree-4 minimax polynomial generated by Sollya with the following
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// commands:
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// > display = hexadecimal;
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// > P = fpminimax((10^x - 1)/x, 3, [|SG...|], [-2^-4, 2^-4]);
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// > 1 + x * P;
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float exp10_lo = fputil::polyeval(lo, 0x1p+0f, 0x1.26bb14p+1f, 0x1.53526p+1f,
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0x1.04b434p+1f, 0x1.2bcf9ep+0f);
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return {exp2_hi_mid, exp10_lo};
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}
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} // namespace LIBC_NAMESPACE_DECL
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#endif // LIBC_TYPES_HAS_FLOAT16
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#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F16_UTILS_H

‎libc/src/math/generic/CMakeLists.txt‎

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@@ -1477,20 +1477,8 @@ add_entrypoint_object(
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HDRS
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../exp10f16.h
14791479
DEPENDS
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.expxf16
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libc.hdr.errno_macros
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libc.hdr.fenv_macros
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libc.src.__support.CPP.array
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libc.src.__support.FPUtil.cast
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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.FPUtil.multiply_add
1489-
libc.src.__support.FPUtil.nearest_integer
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libc.src.__support.FPUtil.polyeval
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libc.src.__support.FPUtil.rounding_mode
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libc.src.__support.macros.optimization
1493-
libc.src.__support.macros.properties.cpu_features
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libc.src.__support.math.exp10f16
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libc.src.errno.errno
14941482
)
14951483

14961484
add_entrypoint_object(
@@ -1519,7 +1507,6 @@ add_entrypoint_object(
15191507
HDRS
15201508
../exp10m1f16.h
15211509
DEPENDS
1522-
.expxf16
15231510
libc.hdr.errno_macros
15241511
libc.hdr.fenv_macros
15251512
libc.src.__support.FPUtil.cast
@@ -1531,6 +1518,7 @@ add_entrypoint_object(
15311518
libc.src.__support.FPUtil.rounding_mode
15321519
libc.src.__support.macros.optimization
15331520
libc.src.__support.macros.properties.cpu_features
1521+
libc.src.__support.math.exp10f16_utils
15341522
)
15351523

15361524
add_entrypoint_object(
@@ -5023,10 +5011,11 @@ add_header_library(
50235011
HDRS
50245012
expxf16.h
50255013
DEPENDS
5026-
libc.src.__support.FPUtil.cast
50275014
libc.src.__support.FPUtil.fp_bits
5015+
libc.src.__support.FPUtil.cast
50285016
libc.src.__support.FPUtil.multiply_add
50295017
libc.src.__support.FPUtil.nearest_integer
50305018
libc.src.__support.macros.attributes
50315019
libc.src.__support.math.expf16_utils
5020+
libc.src.__support.math.exp10_float16_constants
50325021
)

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