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[libc][math][c23] Add log2f16 C23 math function (#106084)
Part of #95250.
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//===-- Half-precision log2(x) 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 | ||
// | ||
//===----------------------------------------------------------------------===// | ||
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#include "src/math/log2f16.h" | ||
#include "expxf16.h" | ||
#include "hdr/errno_macros.h" | ||
#include "hdr/fenv_macros.h" | ||
#include "src/__support/FPUtil/FEnvImpl.h" | ||
#include "src/__support/FPUtil/FPBits.h" | ||
#include "src/__support/FPUtil/PolyEval.h" | ||
#include "src/__support/FPUtil/cast.h" | ||
#include "src/__support/FPUtil/except_value_utils.h" | ||
#include "src/__support/FPUtil/multiply_add.h" | ||
#include "src/__support/common.h" | ||
#include "src/__support/macros/config.h" | ||
#include "src/__support/macros/optimization.h" | ||
#include "src/__support/macros/properties/cpu_features.h" | ||
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namespace LIBC_NAMESPACE_DECL { | ||
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#ifdef LIBC_TARGET_CPU_HAS_FMA | ||
static constexpr size_t N_LOG2F16_EXCEPTS = 2; | ||
#else | ||
static constexpr size_t N_LOG2F16_EXCEPTS = 9; | ||
#endif | ||
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static constexpr fputil::ExceptValues<float16, N_LOG2F16_EXCEPTS> | ||
LOG2F16_EXCEPTS = {{ | ||
// (input, RZ output, RU offset, RD offset, RN offset) | ||
#ifndef LIBC_TARGET_CPU_HAS_FMA | ||
// x = 0x1.224p-1, log2f16(x) = -0x1.a34p-1 (RZ) | ||
{0x3889U, 0xba8dU, 0U, 1U, 0U}, | ||
// x = 0x1.e34p-1, log2f16(x) = -0x1.558p-4 (RZ) | ||
{0x3b8dU, 0xad56U, 0U, 1U, 0U}, | ||
#endif | ||
// x = 0x1.e8cp-1, log2f16(x) = -0x1.128p-4 (RZ) | ||
{0x3ba3U, 0xac4aU, 0U, 1U, 0U}, | ||
#ifndef LIBC_TARGET_CPU_HAS_FMA | ||
// x = 0x1.f98p-1, log2f16(x) = -0x1.2ep-6 (RZ) | ||
{0x3be6U, 0xa4b8U, 0U, 1U, 0U}, | ||
// x = 0x1.facp-1, log2f16(x) = -0x1.e7p-7 (RZ) | ||
{0x3bebU, 0xa39cU, 0U, 1U, 1U}, | ||
#endif | ||
// x = 0x1.fb4p-1, log2f16(x) = -0x1.b88p-7 (RZ) | ||
{0x3bedU, 0xa2e2U, 0U, 1U, 1U}, | ||
#ifndef LIBC_TARGET_CPU_HAS_FMA | ||
// x = 0x1.fecp-1, log2f16(x) = -0x1.cep-9 (RZ) | ||
{0x3bfbU, 0x9b38U, 0U, 1U, 1U}, | ||
// x = 0x1.ffcp-1, log2f16(x) = -0x1.714p-11 (RZ) | ||
{0x3bffU, 0x91c5U, 0U, 1U, 1U}, | ||
// x = 0x1.224p+0, log2f16(x) = 0x1.72cp-3 (RZ) | ||
{0x3c89U, 0x31cbU, 1U, 0U, 1U}, | ||
#endif | ||
}}; | ||
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LLVM_LIBC_FUNCTION(float16, log2f16, (float16 x)) { | ||
using FPBits = fputil::FPBits<float16>; | ||
FPBits x_bits(x); | ||
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uint16_t x_u = x_bits.uintval(); | ||
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// If x <= 0, or x is 1, or x is +inf, or x is NaN. | ||
if (LIBC_UNLIKELY(x_u == 0U || x_u == 0x3c00U || x_u >= 0x7c00U)) { | ||
// log2(NaN) = NaN | ||
if (x_bits.is_nan()) { | ||
if (x_bits.is_signaling_nan()) { | ||
fputil::raise_except_if_required(FE_INVALID); | ||
return FPBits::quiet_nan().get_val(); | ||
} | ||
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return x; | ||
} | ||
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// log2(+/-0) = −inf | ||
if ((x_u & 0x7fffU) == 0U) { | ||
fputil::raise_except_if_required(FE_DIVBYZERO); | ||
return FPBits::inf(Sign::NEG).get_val(); | ||
} | ||
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if (x_u == 0x3c00U) | ||
return FPBits::zero().get_val(); | ||
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// When x < 0. | ||
if (x_u > 0x8000U) { | ||
fputil::set_errno_if_required(EDOM); | ||
fputil::raise_except_if_required(FE_INVALID); | ||
return FPBits::quiet_nan().get_val(); | ||
} | ||
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// log2(+inf) = +inf | ||
return FPBits::inf().get_val(); | ||
} | ||
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if (auto r = LOG2F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value())) | ||
return r.value(); | ||
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// To compute log2(x), we perform the following range reduction: | ||
// x = 2^m * 1.mant, | ||
// log2(x) = m + log2(1.mant). | ||
// To compute log2(1.mant), let f be the highest 6 bits including the hidden | ||
// bit, and d be the difference (1.mant - f), i.e., the remaining 5 bits of | ||
// the mantissa, then: | ||
// log2(1.mant) = log2(f) + log2(1.mant / f) | ||
// = log2(f) + log2(1 + d/f) | ||
// since d/f is sufficiently small. | ||
// We store log2(f) and 1/f in the lookup tables LOG2F_F and ONE_OVER_F_F | ||
// respectively. | ||
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int m = -FPBits::EXP_BIAS; | ||
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// When x is subnormal, normalize it. | ||
if ((x_u & FPBits::EXP_MASK) == 0U) { | ||
// Can't pass an integer to fputil::cast directly. | ||
constexpr float NORMALIZE_EXP = 1U << FPBits::FRACTION_LEN; | ||
x_bits = FPBits(x_bits.get_val() * fputil::cast<float16>(NORMALIZE_EXP)); | ||
x_u = x_bits.uintval(); | ||
m -= FPBits::FRACTION_LEN; | ||
} | ||
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uint16_t mant = x_bits.get_mantissa(); | ||
// Leading 10 - 5 = 5 bits of the mantissa. | ||
int f = mant >> 5; | ||
// Unbiased exponent. | ||
m += x_u >> FPBits::FRACTION_LEN; | ||
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// Set bits to 1.mant instead of 2^m * 1.mant. | ||
x_bits.set_biased_exponent(FPBits::EXP_BIAS); | ||
float mant_f = x_bits.get_val(); | ||
// v = 1.mant * 1/f - 1 = d/f | ||
float v = fputil::multiply_add(mant_f, ONE_OVER_F_F[f], -1.0f); | ||
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// Degree-3 minimax polynomial generated by Sollya with the following | ||
// commands: | ||
// > display = hexadecimal; | ||
// > P = fpminimax(log2(1 + x)/x, 2, [|SG...|], [-2^-5, 2^-5]); | ||
// > x * P; | ||
float log2p1_d_over_f = | ||
v * fputil::polyeval(v, 0x1.715476p+0f, -0x1.71771ap-1f, 0x1.ecb38ep-2f); | ||
// log2(1.mant) = log2(f) + log2(1 + d/f) | ||
float log2_1_mant = LOG2F_F[f] + log2p1_d_over_f; | ||
return fputil::cast<float16>(static_cast<float>(m) + log2_1_mant); | ||
} | ||
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} // namespace LIBC_NAMESPACE_DECL |
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//===-- Implementation header for log2f16 -----------------------*- C++ -*-===// | ||
// | ||
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. | ||
// See https://llvm.org/LICENSE.txt for license information. | ||
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception | ||
// | ||
//===----------------------------------------------------------------------===// | ||
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#ifndef LLVM_LIBC_SRC_MATH_LOG2F16_H | ||
#define LLVM_LIBC_SRC_MATH_LOG2F16_H | ||
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#include "src/__support/macros/config.h" | ||
#include "src/__support/macros/properties/types.h" | ||
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namespace LIBC_NAMESPACE_DECL { | ||
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float16 log2f16(float16 x); | ||
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} // namespace LIBC_NAMESPACE_DECL | ||
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#endif // LLVM_LIBC_SRC_MATH_LOG2F16_H |
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//===-- Exhaustive test for log2f16 ---------------------------------------===// | ||
// | ||
// 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 | ||
// | ||
//===----------------------------------------------------------------------===// | ||
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#include "src/math/log2f16.h" | ||
#include "test/UnitTest/FPMatcher.h" | ||
#include "test/UnitTest/Test.h" | ||
#include "utils/MPFRWrapper/MPFRUtils.h" | ||
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using LlvmLibcLog2f16Test = LIBC_NAMESPACE::testing::FPTest<float16>; | ||
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namespace mpfr = LIBC_NAMESPACE::testing::mpfr; | ||
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// Range: [0, Inf]; | ||
static constexpr uint16_t POS_START = 0x0000U; | ||
static constexpr uint16_t POS_STOP = 0x7c00U; | ||
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// Range: [-Inf, 0]; | ||
static constexpr uint16_t NEG_START = 0x8000U; | ||
static constexpr uint16_t NEG_STOP = 0xfc00U; | ||
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TEST_F(LlvmLibcLog2f16Test, PositiveRange) { | ||
for (uint16_t v = POS_START; v <= POS_STOP; ++v) { | ||
float16 x = FPBits(v).get_val(); | ||
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Log2, x, | ||
LIBC_NAMESPACE::log2f16(x), 0.5); | ||
} | ||
} | ||
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TEST_F(LlvmLibcLog2f16Test, NegativeRange) { | ||
for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) { | ||
float16 x = FPBits(v).get_val(); | ||
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Log2, x, | ||
LIBC_NAMESPACE::log2f16(x), 0.5); | ||
} | ||
} |
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