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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
//
//===----------------------------------------------------------------------===//
#include "src/math/expf16.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/rounding_mode.h"
#include "src/__support/common.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h"
namespace LIBC_NAMESPACE_DECL {
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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},
}};
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},
}};
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
LLVM_LIBC_FUNCTION(float16, expf16, (float16 x)) {
using FPBits = fputil::FPBits<float16>;
FPBits x_bits(x);
uint16_t x_u = x_bits.uintval();
uint16_t x_abs = x_u & 0x7fffU;
// 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();
}
return x;
}
// When x >= 12.
if (x_bits.is_pos() && x_abs >= 0x4a00U) {
// exp(+inf) = +inf
if (x_bits.is_inf())
return FPBits::inf().get_val();
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();
}
}
// When x <= -18.
if (x_u >= 0xcc80U) {
// exp(-inf) = +0
if (x_bits.is_inf())
return FPBits::zero().get_val();
fputil::set_errno_if_required(ERANGE);
fputil::raise_except_if_required(FE_UNDERFLOW | FE_INEXACT);
switch (fputil::quick_get_round()) {
case FE_UPWARD:
return FPBits::min_subnormal().get_val();
default:
return FPBits::zero().get_val();
}
}
// When 0 < |x| <= 2^(-5).
if (x_abs <= 0x2800U && !x_bits.is_zero()) {
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
if (auto r = EXPF16_EXCEPTS_LO.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
return r.value();
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
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;
return fputil::cast<float16>(
fputil::polyeval(xf, 0x1p+0f, 0x1p+0f, 0x1.0004p-1f, 0x1.555778p-3f));
}
}
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
if (auto r = EXPF16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
return r.value();
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
// exp(x) = exp(hi + mid) * exp(lo)
auto [exp_hi_mid, exp_lo] = exp_range_reduction(x);
return fputil::cast<float16>(exp_hi_mid * exp_lo);
}
} // namespace LIBC_NAMESPACE_DECL
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