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[libc][math][c23] Add expf16 C23 math function #100632
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//===-- Implementation header for expf16 ------------------------*- 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_EXPF16_H | ||
#define LLVM_LIBC_SRC_MATH_EXPF16_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 expf16(float16 x); | ||
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} // namespace LIBC_NAMESPACE_DECL | ||
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#endif // LLVM_LIBC_SRC_MATH_EXPF16_H |
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//===-- Half-precision e^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/expf16.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, 2> EXPF16_EXCEPTS_LO = {{ | ||
// (input, RZ output, RU offset, RD offset, RN offset) | ||
// x = 0x1.de4p-8, expf16(x) = 0x1.01cp+0 (RZ) | ||
{0x1f79U, 0x3c07U, 1U, 0U, 0U}, | ||
// x = 0x1.73cp-6, expf16(x) = 0x1.05cp+0 (RZ) | ||
{0x25cfU, 0x3c17U, 1U, 0U, 0U}, | ||
}}; | ||
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static constexpr fputil::ExceptValues<float16, 3> EXPF16_EXCEPTS_HI = {{ | ||
// (input, RZ output, RU offset, RD offset, RN offset) | ||
// x = 0x1.c34p+0, expf16(x) = 0x1.74cp+2 (RZ) | ||
{0x3f0dU, 0x45d3U, 1U, 0U, 1U}, | ||
// x = -0x1.488p-5, expf16(x) = 0x1.ebcp-1 (RZ) | ||
{0xa922U, 0x3bafU, 1U, 0U, 0U}, | ||
// x = -0x1.55p-5, expf16(x) = 0x1.ebp-1 (RZ) | ||
{0xa954U, 0x3bacU, 1U, 0U, 0U}, | ||
}}; | ||
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// Generated by Sollya with the following commands: | ||
// > display = hexadecimal; | ||
// > for i from -18 to 12 do print(round(exp(i), SG, RN)); | ||
static constexpr cpp::array<float, 31> EXP_HI = { | ||
0x1.05a628p-26f, 0x1.639e32p-25f, 0x1.e355bcp-24f, 0x1.4875cap-22f, | ||
0x1.be6c7p-21f, 0x1.2f6054p-19f, 0x1.9c54c4p-18f, 0x1.183542p-16f, | ||
0x1.7cd79cp-15f, 0x1.02cf22p-13f, 0x1.5fc21p-12f, 0x1.de16bap-11f, | ||
0x1.44e52p-9f, 0x1.b993fep-8f, 0x1.2c155cp-6f, 0x1.97db0cp-5f, | ||
0x1.152aaap-3f, 0x1.78b564p-2f, 0x1p+0f, 0x1.5bf0a8p+1f, | ||
0x1.d8e64cp+2f, 0x1.415e5cp+4f, 0x1.b4c902p+5f, 0x1.28d38ap+7f, | ||
0x1.936dc6p+8f, 0x1.122886p+10f, 0x1.749ea8p+11f, 0x1.fa7158p+12f, | ||
0x1.5829dcp+14f, 0x1.d3c448p+15f, 0x1.3de166p+17f, | ||
}; | ||
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// Generated by Sollya with the following commands: | ||
// > display = hexadecimal; | ||
// > for i from 0 to 7 do print(round(exp(i * 2^-3), SG, RN)); | ||
static constexpr cpp::array<float, 8> EXP_MID = { | ||
0x1p+0f, 0x1.221604p+0f, 0x1.48b5e4p+0f, 0x1.747a52p+0f, | ||
0x1.a61298p+0f, 0x1.de455ep+0f, 0x1.0ef9dcp+1f, 0x1.330e58p+1f, | ||
}; | ||
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LLVM_LIBC_FUNCTION(float16, expf16, (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 0 < |x| <= 2^(-5), or |x| >= 12, or x is NaN. | ||
if (LIBC_UNLIKELY(x_abs <= 0x2800U || x_abs >= 0x4a00U)) { | ||
// exp(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 >= 12. | ||
if (x_bits.is_pos() && x_abs >= 0x4a00U) { | ||
// exp(+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 <= -18. | ||
if (x_u >= 0xcc80U) { | ||
// exp(-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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switch (fputil::quick_get_round()) { | ||
case FE_UPWARD: | ||
return FPBits::min_subnormal().get_val(); | ||
default: | ||
return FPBits::zero().get_val(); | ||
} | ||
} | ||
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// When 0 < |x| <= 2^(-5). | ||
if (x_abs <= 0x2800U && !x_bits.is_zero()) { | ||
if (auto r = EXPF16_EXCEPTS_LO.lookup(x_u); LIBC_UNLIKELY(r.has_value())) | ||
return r.value(); | ||
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float xf = x; | ||
// Degree-3 minimax polynomial generated by Sollya with the following | ||
// commands: | ||
// > display = hexadecimal; | ||
// > P = fpminimax(expm1(x)/x, 2, [|SG...|], [-2^-5, 2^-5]); | ||
// > 1 + x * P; | ||
float r = | ||
fputil::polyeval(xf, 0x1p+0f, 0x1p+0f, 0x1.0004p-1f, 0x1.555778p-3f); | ||
return static_cast<float16>(r); | ||
} | ||
} | ||
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if (auto r = EXPF16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value())) | ||
return r.value(); | ||
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// For -18 < x < 12, to compute exp(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, | ||
// exp(x) = exp(hi + mid + lo) = exp(hi) * exp(mid) * exp(lo). | ||
// We store exp(hi) and exp(mid) in the lookup tables EXP_HI and EXP_MID | ||
// respectively. exp(lo) is computed using a degree-3 minimax polynomial | ||
// generated by Sollya. | ||
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float xf = static_cast<float>(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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float exp_hi = EXP_HI[x_hi + 18]; | ||
float exp_mid = EXP_MID[x_mid]; | ||
// Degree-3 minimax polynomial generated by Sollya with the following | ||
// commands: | ||
// > display = hexadecimal; | ||
// > P = fpminimax(expm1(x)/x, 2, [|SG...|], [-2^-4, 2^-4]); | ||
// > 1 + x * P; | ||
float exp_lo = | ||
fputil::polyeval(lo, 0x1p+0f, 0x1p+0f, 0x1.001p-1f, 0x1.555ddep-3f); | ||
return static_cast<float16>(exp_hi * exp_mid * exp_lo); | ||
} | ||
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} // namespace LIBC_NAMESPACE_DECL |
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Original file line number | Diff line number | Diff line change |
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//===-- Exhaustive test for expf16 ----------------------------------------===// | ||
// | ||
// 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/expf16.h" | ||
#include "test/UnitTest/FPMatcher.h" | ||
#include "test/UnitTest/Test.h" | ||
#include "utils/MPFRWrapper/MPFRUtils.h" | ||
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using LlvmLibcExpf16Test = 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(LlvmLibcExpf16Test, PositiveRange) { | ||
for (uint16_t v = POS_START; v <= POS_STOP; ++v) { | ||
float16 x = FPBits(v).get_val(); | ||
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Exp, x, | ||
LIBC_NAMESPACE::expf16(x), 0.5); | ||
} | ||
} | ||
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TEST_F(LlvmLibcExpf16Test, NegativeRange) { | ||
for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) { | ||
float16 x = FPBits(v).get_val(); | ||
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Exp, x, | ||
LIBC_NAMESPACE::expf16(x), 0.5); | ||
} | ||
} |
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Can we call
1 + x + P
a minimax polynomial too, or onlyP
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yes, we can, it is for sure minimax with respect to some metric