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1 change: 1 addition & 0 deletions libc/shared/math.h
Original file line number Diff line number Diff line change
Expand Up @@ -56,6 +56,7 @@
#include "math/expf16.h"
#include "math/expm1.h"
#include "math/expm1f.h"
#include "math/expm1f16.h"
#include "math/frexpf.h"
#include "math/frexpf128.h"
#include "math/frexpf16.h"
Expand Down
29 changes: 29 additions & 0 deletions libc/shared/math/expm1f16.h
Original file line number Diff line number Diff line change
@@ -0,0 +1,29 @@
//===-- Shared expm1f16 function --------------------------------*- 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
//
//===----------------------------------------------------------------------===//

#ifndef LLVM_LIBC_SHARED_MATH_EXPM1F16_H
#define LLVM_LIBC_SHARED_MATH_EXPM1F16_H

#include "include/llvm-libc-macros/float16-macros.h"
#include "shared/libc_common.h"

#ifdef LIBC_TYPES_HAS_FLOAT16

#include "src/__support/math/expm1f16.h"

namespace LIBC_NAMESPACE_DECL {
namespace shared {

using math::expm1f16;

} // namespace shared
} // namespace LIBC_NAMESPACE_DECL

#endif // LIBC_TYPES_HAS_FLOAT16

#endif // LLVM_LIBC_SHARED_MATH_EXPM1F16_H
16 changes: 16 additions & 0 deletions libc/src/__support/math/CMakeLists.txt
Original file line number Diff line number Diff line change
Expand Up @@ -923,6 +923,22 @@ add_header_library(
libc.src.errno.errno
)

add_header_library(
expm1f16
HDRS
expm1f16.h
DEPENDS
.expxf16_utils
libc.src.__support.FPUtil.cast
libc.src.__support.FPUtil.except_value_utils
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
)

add_header_library(
range_reduction_double
HDRS
Expand Down
153 changes: 153 additions & 0 deletions libc/src/__support/math/expm1f16.h
Original file line number Diff line number Diff line change
@@ -0,0 +1,153 @@
//===-- Implementation header for expm1f16 ----------------------*- 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
//
//===----------------------------------------------------------------------===//

#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXPM1F16_H
#define LLVM_LIBC_SRC___SUPPORT_MATH_EXPM1F16_H

#include "include/llvm-libc-macros/float16-macros.h"

#ifdef LIBC_TYPES_HAS_FLOAT16

#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/math/expxf16_utils.h"

namespace LIBC_NAMESPACE_DECL {

namespace math {

LIBC_INLINE static constexpr float16 expm1f16(float16 x) {
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
constexpr fputil::ExceptValues<float16, 1> EXPM1F16_EXCEPTS_LO = {{
// (input, RZ output, RU offset, RD offset, RN offset)
// x = 0x1.564p-5, expm1f16(x) = 0x1.5d4p-5 (RZ)
{0x2959U, 0x2975U, 1U, 0U, 1U},
}};

#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT
constexpr size_t N_EXPM1F16_EXCEPTS_HI = 2;
#else
constexpr size_t N_EXPM1F16_EXCEPTS_HI = 3;
#endif

constexpr fputil::ExceptValues<float16, N_EXPM1F16_EXCEPTS_HI>
EXPM1F16_EXCEPTS_HI = {{
// (input, RZ output, RU offset, RD offset, RN offset)
// x = 0x1.c34p+0, expm1f16(x) = 0x1.34cp+2 (RZ)
{0x3f0dU, 0x44d3U, 1U, 0U, 1U},
// x = -0x1.e28p-3, expm1f16(x) = -0x1.adcp-3 (RZ)
{0xb38aU, 0xb2b7U, 0U, 1U, 1U},
#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
// x = 0x1.a08p-3, exp10m1f(x) = 0x1.cdcp-3 (RZ)
{0x3282U, 0x3337U, 1U, 0U, 0U},
#endif
}};
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS

using namespace math::expxf16_internal;
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 * log(2), or x is NaN.
if (LIBC_UNLIKELY(x_abs <= 0x3000U || x_abs >= 0x47a0U)) {
// expm1(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;
}

// expm1(+/-0) = +/-0
if (x_abs == 0)
return x;

// When x >= 16 * log(2).
if (x_bits.is_pos() && x_abs >= 0x498cU) {
// expm1(+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 * log(2).
if (x_u >= 0xc7a0U) {
// expm1(-inf) = -1
if (x_bits.is_inf())
return FPBits::one(Sign::NEG).get_val();

// When x > -0x1.0ap+3, round(expm1(x), HP, RN) = -1.
if (x_u > 0xc828U)
return fputil::round_result_slightly_up(
FPBits::one(Sign::NEG).get_val());
// When x <= -0x1.0ap+3, round(expm1(x), HP, RN) = -0x1.ffcp-1.
return fputil::round_result_slightly_down(
fputil::cast<float16>(-0x1.ffcp-1));
}

// When 0 < |x| <= 2^(-3).
if (x_abs <= 0x3000U && !x_bits.is_zero()) {

#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
if (auto r = EXPM1F16_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(expm1(x)/x, 4, [|SG...|], [-2^-3, 2^-3]);
// > x * P;
return fputil::cast<float16>(
xf * fputil::polyeval(xf, 0x1p+0f, 0x1.fffff8p-2f, 0x1.555556p-3f,
0x1.55905ep-5f, 0x1.1124c2p-7f));
}
}

#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
if (auto r = EXPM1F16_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);
// expm1(x) = exp(hi + mid) * exp(lo) - 1
return fputil::cast<float16>(fputil::multiply_add(exp_hi_mid, exp_lo, -1.0f));
}

} // namespace math

} // namespace LIBC_NAMESPACE_DECL

#endif // LIBC_TYPES_HAS_FLOAT16

#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXPM1F16_H
12 changes: 1 addition & 11 deletions libc/src/math/generic/CMakeLists.txt
Original file line number Diff line number Diff line change
Expand Up @@ -1571,17 +1571,7 @@ add_entrypoint_object(
HDRS
../expm1f16.h
DEPENDS
libc.hdr.errno_macros
libc.hdr.fenv_macros
libc.src.__support.FPUtil.cast
libc.src.__support.FPUtil.except_value_utils
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
libc.src.__support.math.expxf16_utils
libc.src.__support.math.expm1f16
)

add_entrypoint_object(
Expand Down
130 changes: 2 additions & 128 deletions libc/src/math/generic/expm1f16.cpp
Original file line number Diff line number Diff line change
Expand Up @@ -7,135 +7,9 @@
//===----------------------------------------------------------------------===//

#include "src/math/expm1f16.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/math/expxf16_utils.h"
#include "src/__support/math/expm1f16.h"

namespace LIBC_NAMESPACE_DECL {

#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
static constexpr fputil::ExceptValues<float16, 1> EXPM1F16_EXCEPTS_LO = {{
// (input, RZ output, RU offset, RD offset, RN offset)
// x = 0x1.564p-5, expm1f16(x) = 0x1.5d4p-5 (RZ)
{0x2959U, 0x2975U, 1U, 0U, 1U},
}};

#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT
static constexpr size_t N_EXPM1F16_EXCEPTS_HI = 2;
#else
static constexpr size_t N_EXPM1F16_EXCEPTS_HI = 3;
#endif

static constexpr fputil::ExceptValues<float16, N_EXPM1F16_EXCEPTS_HI>
EXPM1F16_EXCEPTS_HI = {{
// (input, RZ output, RU offset, RD offset, RN offset)
// x = 0x1.c34p+0, expm1f16(x) = 0x1.34cp+2 (RZ)
{0x3f0dU, 0x44d3U, 1U, 0U, 1U},
// x = -0x1.e28p-3, expm1f16(x) = -0x1.adcp-3 (RZ)
{0xb38aU, 0xb2b7U, 0U, 1U, 1U},
#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
// x = 0x1.a08p-3, exp10m1f(x) = 0x1.cdcp-3 (RZ)
{0x3282U, 0x3337U, 1U, 0U, 0U},
#endif
}};
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS

LLVM_LIBC_FUNCTION(float16, expm1f16, (float16 x)) {
using namespace math::expxf16_internal;
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 * log(2), or x is NaN.
if (LIBC_UNLIKELY(x_abs <= 0x3000U || x_abs >= 0x47a0U)) {
// expm1(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;
}

// expm1(+/-0) = +/-0
if (x_abs == 0)
return x;

// When x >= 16 * log(2).
if (x_bits.is_pos() && x_abs >= 0x498cU) {
// expm1(+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 * log(2).
if (x_u >= 0xc7a0U) {
// expm1(-inf) = -1
if (x_bits.is_inf())
return FPBits::one(Sign::NEG).get_val();

// When x > -0x1.0ap+3, round(expm1(x), HP, RN) = -1.
if (x_u > 0xc828U)
return fputil::round_result_slightly_up(
FPBits::one(Sign::NEG).get_val());
// When x <= -0x1.0ap+3, round(expm1(x), HP, RN) = -0x1.ffcp-1.
return fputil::round_result_slightly_down(
fputil::cast<float16>(-0x1.ffcp-1));
}

// When 0 < |x| <= 2^(-3).
if (x_abs <= 0x3000U && !x_bits.is_zero()) {

#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
if (auto r = EXPM1F16_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(expm1(x)/x, 4, [|SG...|], [-2^-3, 2^-3]);
// > x * P;
return fputil::cast<float16>(
xf * fputil::polyeval(xf, 0x1p+0f, 0x1.fffff8p-2f, 0x1.555556p-3f,
0x1.55905ep-5f, 0x1.1124c2p-7f));
}
}

#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
if (auto r = EXPM1F16_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);
// expm1(x) = exp(hi + mid) * exp(lo) - 1
return fputil::cast<float16>(fputil::multiply_add(exp_hi_mid, exp_lo, -1.0f));
}
LLVM_LIBC_FUNCTION(float16, expm1f16, (float16 x)) { return math::expm1f16(x); }

} // namespace LIBC_NAMESPACE_DECL
1 change: 1 addition & 0 deletions libc/test/shared/CMakeLists.txt
Original file line number Diff line number Diff line change
Expand Up @@ -47,6 +47,7 @@ add_fp_unittest(
libc.src.__support.math.exp2m1f16
libc.src.__support.math.expm1
libc.src.__support.math.expm1f
libc.src.__support.math.expm1f16
libc.src.__support.math.exp10
libc.src.__support.math.exp10f
libc.src.__support.math.exp10f16
Expand Down
1 change: 1 addition & 0 deletions libc/test/shared/shared_math_test.cpp
Original file line number Diff line number Diff line change
Expand Up @@ -31,6 +31,7 @@ TEST(LlvmLibcSharedMathTest, AllFloat16) {
EXPECT_FP_EQ(0x1p+0f16, LIBC_NAMESPACE::shared::exp2f16(0.0f16));
EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::exp2m1f16(0.0f16));
EXPECT_FP_EQ(0x1p+0f16, LIBC_NAMESPACE::shared::expf16(0.0f16));
EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::expm1f16(0.0f16));

ASSERT_FP_EQ(float16(8 << 5), LIBC_NAMESPACE::shared::ldexpf16(8.0f16, 5));
ASSERT_FP_EQ(float16(-1 * (8 << 5)),
Expand Down
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