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//===-- Half-precision asinh(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/asinhf16.h"
#include "explogxf.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/FPUtil/rounding_mode.h"
#include "src/__support/FPUtil/sqrt.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 size_t N_EXCEPTS = 8;
static constexpr fputil::ExceptValues<float16, N_EXCEPTS> ASINHF16_EXCEPTS{{
// (input, RZ output, RU offset, RD offset, RN offset)
// x = 0x1.da4p-2, asinhf16(x) = 0x1.ca8p-2 (RZ)
{0x3769, 0x372a, 1, 0, 1},
// x = 0x1.d6cp-1, asinhf16(x) = 0x1.a58p-1 (RZ)
{0x3b5b, 0x3a96, 1, 0, 0},
// x = 0x1.c7cp+3, asinhf16(x) = 0x1.accp+1 (RZ)
{0x4b1f, 0x42b3, 1, 0, 0},
// x = 0x1.26cp+4, asinhf16(x) = 0x1.cd8p+1 (RZ)
{0x4c9b, 0x4336, 1, 0, 1},
// x = -0x1.da4p-2, asinhf16(x) = -0x1.ca8p-2 (RZ)
{0xb769, 0xb72a, 0, 1, 1},
// x = -0x1.d6cp-1, asinhf16(x) = -0x1.a58p-1 (RZ)
{0xbb5b, 0xba96, 0, 1, 0},
// x = -0x1.c7cp+3, asinhf16(x) = -0x1.accp+1 (RZ)
{0xcb1f, 0xc2b3, 0, 1, 0},
// x = -0x1.26cp+4, asinhf16(x) = -0x1.cd8p+1 (RZ)
{0xcc9b, 0xc336, 0, 1, 1},
}};
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
LLVM_LIBC_FUNCTION(float16, asinhf16, (float16 x)) {
using namespace acoshf_internal;
using FPBits = fputil::FPBits<float16>;
FPBits xbits(x);
uint16_t x_u = xbits.uintval();
uint16_t x_abs = x_u & 0x7fff;
if (LIBC_UNLIKELY(xbits.is_inf_or_nan())) {
if (xbits.is_signaling_nan()) {
fputil::raise_except_if_required(FE_INVALID);
return FPBits::quiet_nan().get_val();
}
return x;
}
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
// Handle exceptional values
if (auto r = ASINHF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
return r.value();
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
float xf = x;
const float SIGN[2] = {1.0f, -1.0f};
float x_sign = SIGN[x_u >> 15];
// |x| <= 0.25
if (LIBC_UNLIKELY(x_abs <= 0x3400)) {
// when |x| < 0x1.718p-5, asinhf16(x) = x. Adjust by 1 ULP for certain
// rounding types.
if (LIBC_UNLIKELY(x_abs < 0x29c6)) {
int rounding = fputil::quick_get_round();
if ((rounding == FE_UPWARD || rounding == FE_TOWARDZERO) && xf < 0)
return fputil::cast<float16>(xf + 0x1p-24f);
if ((rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO) && xf > 0)
return fputil::cast<float16>(xf - 0x1p-24f);
return fputil::cast<float16>(xf);
}
float x_sq = xf * xf;
// Generated by Sollya with:
// > P = fpminimax(asinh(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 2^-2]);
// The last coefficient 0x1.bd114ep-6f has been changed to 0x1.bd114ep-5f
// for better accuracy.
float p = fputil::polyeval(x_sq, 1.0f, -0x1.555552p-3f, 0x1.332f6ap-4f,
-0x1.6c53dep-5f, 0x1.bd114ep-5f);
return fputil::cast<float16>(xf * p);
}
// General case: asinh(x) = ln(x + sqrt(x^2 + 1))
float sqrt_term = fputil::sqrt<float>(fputil::multiply_add(xf, xf, 1.0f));
return fputil::cast<float16>(
x_sign * log_eval(fputil::multiply_add(xf, x_sign, sqrt_term)));
}
} // namespace LIBC_NAMESPACE_DECL
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