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[libc][math][c23] Add exp2f16 C23 math function (llvm#101217)
Part of llvm#95250.
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//===-- Implementation header for exp2f16 -----------------------*- 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_EXP2F16_H | ||
#define LLVM_LIBC_SRC_MATH_EXP2F16_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 exp2f16(float16 x); | ||
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} // namespace LIBC_NAMESPACE_DECL | ||
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#endif // LLVM_LIBC_SRC_MATH_EXP2F16_H |
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//===-- Half-precision 2^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/exp2f16.h" | ||
#include "hdr/errno_macros.h" | ||
#include "hdr/fenv_macros.h" | ||
#include "src/__support/CPP/array.h" | ||
#include "src/__support/FPUtil/FEnvImpl.h" | ||
#include "src/__support/FPUtil/FPBits.h" | ||
#include "src/__support/FPUtil/PolyEval.h" | ||
#include "src/__support/FPUtil/except_value_utils.h" | ||
#include "src/__support/FPUtil/multiply_add.h" | ||
#include "src/__support/FPUtil/nearest_integer.h" | ||
#include "src/__support/FPUtil/rounding_mode.h" | ||
#include "src/__support/common.h" | ||
#include "src/__support/macros/config.h" | ||
#include "src/__support/macros/optimization.h" | ||
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namespace LIBC_NAMESPACE_DECL { | ||
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static constexpr fputil::ExceptValues<float16, 3> EXP2F16_EXCEPTS = {{ | ||
// (input, RZ output, RU offset, RD offset, RN offset) | ||
// x = 0x1.714p-11, exp2f16(x) = 0x1p+0 (RZ) | ||
{0x11c5U, 0x3c00U, 1U, 0U, 1U}, | ||
// x = -0x1.558p-4, exp2f16(x) = 0x1.e34p-1 (RZ) | ||
{0xad56U, 0x3b8dU, 1U, 0U, 0U}, | ||
// x = -0x1.d5cp-4, exp2f16(x) = 0x1.d8cp-1 (RZ) | ||
{0xaf57U, 0x3b63U, 1U, 0U, 0U}, | ||
}}; | ||
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// Generated by Sollya with the following commands: | ||
// > display = hexadecimal; | ||
// > for i from 0 to 7 do printsingle(round(2^(i * 2^-3), SG, RN)); | ||
static constexpr cpp::array<uint32_t, 8> EXP2_MID_BITS = { | ||
0x3f80'0000U, 0x3f8b'95c2U, 0x3f98'37f0U, 0x3fa5'fed7U, | ||
0x3fb5'04f3U, 0x3fc5'672aU, 0x3fd7'44fdU, 0x3fea'c0c7U, | ||
}; | ||
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LLVM_LIBC_FUNCTION(float16, exp2f16, (float16 x)) { | ||
using FPBits = fputil::FPBits<float16>; | ||
FPBits x_bits(x); | ||
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uint16_t x_u = x_bits.uintval(); | ||
uint16_t x_abs = x_u & 0x7fffU; | ||
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// When |x| >= 16, or x is NaN. | ||
if (LIBC_UNLIKELY(x_abs >= 0x4c00U)) { | ||
// exp2(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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// When x >= 16. | ||
if (x_bits.is_pos()) { | ||
// exp2(+inf) = +inf | ||
if (x_bits.is_inf()) | ||
return FPBits::inf().get_val(); | ||
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switch (fputil::quick_get_round()) { | ||
case FE_TONEAREST: | ||
case FE_UPWARD: | ||
fputil::set_errno_if_required(ERANGE); | ||
fputil::raise_except_if_required(FE_OVERFLOW); | ||
return FPBits::inf().get_val(); | ||
default: | ||
return FPBits::max_normal().get_val(); | ||
} | ||
} | ||
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// When x <= -25. | ||
if (x_u >= 0xce40U) { | ||
// exp2(-inf) = +0 | ||
if (x_bits.is_inf()) | ||
return FPBits::zero().get_val(); | ||
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fputil::set_errno_if_required(ERANGE); | ||
fputil::raise_except_if_required(FE_UNDERFLOW | FE_INEXACT); | ||
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if (fputil::fenv_is_round_up()) | ||
return FPBits::min_subnormal().get_val(); | ||
return FPBits::zero().get_val(); | ||
} | ||
} | ||
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if (auto r = EXP2F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value())) | ||
return r.value(); | ||
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// For -25 < x < 16, to compute 2^x, we perform the following range reduction: | ||
// find hi, mid, lo, such that: | ||
// x = hi + mid + lo, in which | ||
// hi is an integer, | ||
// mid * 2^3 is an integer, | ||
// -2^(-4) <= lo < 2^(-4). | ||
// In particular, | ||
// hi + mid = round(x * 2^3) * 2^(-3). | ||
// Then, | ||
// 2^x = 2^(hi + mid + lo) = 2^hi * 2^mid * 2^lo. | ||
// We store 2^mid in the lookup table EXP2_MID_BITS, and compute 2^hi * 2^mid | ||
// by adding hi to the exponent field of 2^mid. 2^lo is computed using a | ||
// degree-3 minimax polynomial generated by Sollya. | ||
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float xf = x; | ||
float kf = fputil::nearest_integer(xf * 0x1.0p+3f); | ||
int x_hi_mid = static_cast<int>(kf); | ||
int x_hi = x_hi_mid >> 3; | ||
int x_mid = x_hi_mid & 0x7; | ||
// lo = x - (hi + mid) = round(x * 2^3) * (-2^(-3)) + x | ||
float lo = fputil::multiply_add(kf, -0x1.0p-3f, xf); | ||
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uint32_t exp2_hi_mid_bits = | ||
EXP2_MID_BITS[x_mid] + | ||
static_cast<uint32_t>(x_hi << fputil::FPBits<float>::FRACTION_LEN); | ||
float exp2_hi_mid = fputil::FPBits<float>(exp2_hi_mid_bits).get_val(); | ||
// Degree-3 minimax polynomial generated by Sollya with the following | ||
// commands: | ||
// > display = hexadecimal; | ||
// > P = fpminimax((2^x - 1)/x, 2, [|SG...|], [-2^-4, 2^-4]); | ||
// > 1 + x * P; | ||
float exp2_lo = fputil::polyeval(lo, 0x1p+0f, 0x1.62e43p-1f, 0x1.ec0aa6p-3f, | ||
0x1.c6b4a6p-5f); | ||
return static_cast<float16>(exp2_hi_mid * exp2_lo); | ||
} | ||
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} // namespace LIBC_NAMESPACE_DECL |
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//===-- Exhaustive test for exp2f16 ---------------------------------------===// | ||
// | ||
// 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/exp2f16.h" | ||
#include "test/UnitTest/FPMatcher.h" | ||
#include "test/UnitTest/Test.h" | ||
#include "utils/MPFRWrapper/MPFRUtils.h" | ||
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using LlvmLibcExp2f16Test = 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(LlvmLibcExp2f16Test, PositiveRange) { | ||
for (uint16_t v = POS_START; v <= POS_STOP; ++v) { | ||
float16 x = FPBits(v).get_val(); | ||
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Exp2, x, | ||
LIBC_NAMESPACE::exp2f16(x), 0.5); | ||
} | ||
} | ||
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TEST_F(LlvmLibcExp2f16Test, NegativeRange) { | ||
for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) { | ||
float16 x = FPBits(v).get_val(); | ||
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Exp2, x, | ||
LIBC_NAMESPACE::exp2f16(x), 0.5); | ||
} | ||
} |
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//===-- Performance test for exp2f16 --------------------------------------===// | ||
// | ||
// 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 "SingleInputSingleOutputPerf.h" | ||
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#include "src/math/exp2f16.h" | ||
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// LLVM libc might be the only libc implementation with support for float16 math | ||
// functions currently. We can't compare our float16 functions against the | ||
// system libc, so we compare them against this placeholder function. | ||
static float16 placeholderf16(float16 x) { return x; } | ||
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int main() { | ||
SINGLE_INPUT_SINGLE_OUTPUT_PERF_EX(float16, LIBC_NAMESPACE::exp2f16, | ||
::placeholderf16, 20'000, | ||
"exp2f16_perf.log") | ||
} |
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