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//===-- Half-precision 2^x - 1 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/exp2m1f16.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/FPUtil/rounding_mode.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"
namespace LIBC_NAMESPACE_DECL {
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
static constexpr fputil::ExceptValues<float16, 6> EXP2M1F16_EXCEPTS_LO = {{
// (input, RZ output, RU offset, RD offset, RN offset)
// x = 0x1.cf4p-13, exp2m1f16(x) = 0x1.41p-13 (RZ)
{0x0b3dU, 0x0904U, 1U, 0U, 1U},
// x = 0x1.4fcp-12, exp2m1f16(x) = 0x1.d14p-13 (RZ)
{0x0d3fU, 0x0b45U, 1U, 0U, 1U},
// x = 0x1.63p-11, exp2m1f16(x) = 0x1.ec4p-12 (RZ)
{0x118cU, 0x0fb1U, 1U, 0U, 0U},
// x = 0x1.6fp-7, exp2m1f16(x) = 0x1.fe8p-8 (RZ)
{0x21bcU, 0x1ffaU, 1U, 0U, 1U},
// x = -0x1.c6p-10, exp2m1f16(x) = -0x1.3a8p-10 (RZ)
{0x9718U, 0x94eaU, 0U, 1U, 0U},
// x = -0x1.cfcp-10, exp2m1f16(x) = -0x1.414p-10 (RZ)
{0x973fU, 0x9505U, 0U, 1U, 0U},
}};
#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT
static constexpr size_t N_EXP2M1F16_EXCEPTS_HI = 6;
#else
static constexpr size_t N_EXP2M1F16_EXCEPTS_HI = 7;
#endif
static constexpr fputil::ExceptValues<float16, N_EXP2M1F16_EXCEPTS_HI>
EXP2M1F16_EXCEPTS_HI = {{
// (input, RZ output, RU offset, RD offset, RN offset)
// x = 0x1.e58p-3, exp2m1f16(x) = 0x1.6dcp-3 (RZ)
{0x3396U, 0x31b7U, 1U, 0U, 0U},
#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
// x = 0x1.2e8p-2, exp2m1f16(x) = 0x1.d14p-3 (RZ)
{0x34baU, 0x3345U, 1U, 0U, 0U},
#endif
// x = 0x1.ad8p-2, exp2m1f16(x) = 0x1.598p-2 (RZ)
{0x36b6U, 0x3566U, 1U, 0U, 0U},
#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT
// x = 0x1.edcp-2, exp2m1f16(x) = 0x1.964p-2 (RZ)
{0x37b7U, 0x3659U, 1U, 0U, 1U},
#endif
// x = -0x1.804p-3, exp2m1f16(x) = -0x1.f34p-4 (RZ)
{0xb201U, 0xafcdU, 0U, 1U, 1U},
// x = -0x1.f3p-3, exp2m1f16(x) = -0x1.3e4p-3 (RZ)
{0xb3ccU, 0xb0f9U, 0U, 1U, 0U},
// x = -0x1.294p-1, exp2m1f16(x) = -0x1.53p-2 (RZ)
{0xb8a5U, 0xb54cU, 0U, 1U, 1U},
#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
// x = -0x1.a34p-1, exp2m1f16(x) = -0x1.bb4p-2 (RZ)
{0xba8dU, 0xb6edU, 0U, 1U, 1U},
#endif
}};
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
LLVM_LIBC_FUNCTION(float16, exp2m1f16, (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 |x| <= 2^(-3), or |x| >= 11, or x is NaN.
if (LIBC_UNLIKELY(x_abs <= 0x3000U || x_abs >= 0x4980U)) {
// exp2m1(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 >= 16.
if (x_u >= 0x4c00 && x_bits.is_pos()) {
// exp2m1(+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 | FE_INEXACT);
return FPBits::inf().get_val();
default:
return FPBits::max_normal().get_val();
}
}
// When x < -11.
if (x_u > 0xc980U) {
// exp2m1(-inf) = -1
if (x_bits.is_inf())
return FPBits::one(Sign::NEG).get_val();
// When -12 < x < -11, round(2^x - 1, HP, RN) = -0x1.ffcp-1.
if (x_u < 0xca00U)
return fputil::round_result_slightly_down(
fputil::cast<float16>(-0x1.ffcp-1));
// When x <= -12, round(2^x - 1, HP, RN) = -1.
switch (fputil::quick_get_round()) {
case FE_TONEAREST:
case FE_DOWNWARD:
return FPBits::one(Sign::NEG).get_val();
default:
return fputil::cast<float16>(-0x1.ffcp-1);
}
}
// When |x| <= 2^(-3).
if (x_abs <= 0x3000U) {
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
if (auto r = EXP2M1F16_EXCEPTS_LO.lookup(x_u);
LIBC_UNLIKELY(r.has_value()))
return r.value();
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
float xf = x;
// Degree-5 minimax polynomial generated by Sollya with the following
// commands:
// > display = hexadecimal;
// > P = fpminimax((2^x - 1)/x, 4, [|SG...|], [-2^-3, 2^-3]);
// > x * P;
return fputil::cast<float16>(
xf * fputil::polyeval(xf, 0x1.62e43p-1f, 0x1.ebfbdep-3f,
0x1.c6af88p-5f, 0x1.3b45d6p-7f,
0x1.641e7cp-10f));
}
}
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
if (auto r = EXP2M1F16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
return r.value();
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
// exp2(x) = exp2(hi + mid) * exp2(lo)
auto [exp2_hi_mid, exp2_lo] = exp2_range_reduction(x);
// exp2m1(x) = exp2(hi + mid) * exp2(lo) - 1
return fputil::cast<float16>(
fputil::multiply_add(exp2_hi_mid, exp2_lo, -1.0f));
}
} // namespace LIBC_NAMESPACE_DECL
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