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[libc][math][c23] Add expf16 C23 math function #100632

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1 change: 1 addition & 0 deletions libc/config/linux/aarch64/entrypoints.txt
Original file line number Diff line number Diff line change
Expand Up @@ -534,6 +534,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
libc.src.math.canonicalizef16
libc.src.math.ceilf16
libc.src.math.copysignf16
libc.src.math.expf16
libc.src.math.f16add
libc.src.math.f16addf
libc.src.math.f16div
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1 change: 1 addition & 0 deletions libc/config/linux/x86_64/entrypoints.txt
Original file line number Diff line number Diff line change
Expand Up @@ -562,6 +562,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
libc.src.math.canonicalizef16
libc.src.math.ceilf16
libc.src.math.copysignf16
libc.src.math.expf16
libc.src.math.f16add
libc.src.math.f16addf
libc.src.math.f16addl
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2 changes: 1 addition & 1 deletion libc/docs/math/index.rst
Original file line number Diff line number Diff line change
Expand Up @@ -284,7 +284,7 @@ Higher Math Functions
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| erfc | | | | | | 7.12.8.2 | F.10.5.2 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| exp | |check| | |check| | | | | 7.12.6.1 | F.10.3.1 |
| exp | |check| | |check| | | |check| | | 7.12.6.1 | F.10.3.1 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| exp10 | |check| | |check| | | | | 7.12.6.2 | F.10.3.2 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
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1 change: 1 addition & 0 deletions libc/spec/stdc.td
Original file line number Diff line number Diff line change
Expand Up @@ -573,6 +573,7 @@ def StdC : StandardSpec<"stdc"> {

FunctionSpec<"exp", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
FunctionSpec<"expf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
GuardedFunctionSpec<"expf16", RetValSpec<Float16Type>, [ArgSpec<Float16Type>], "LIBC_TYPES_HAS_FLOAT16">,

FunctionSpec<"exp2", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
FunctionSpec<"exp2f", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
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1 change: 1 addition & 0 deletions libc/src/math/CMakeLists.txt
Original file line number Diff line number Diff line change
Expand Up @@ -97,6 +97,7 @@ add_math_entrypoint_object(erff)

add_math_entrypoint_object(exp)
add_math_entrypoint_object(expf)
add_math_entrypoint_object(expf16)

add_math_entrypoint_object(exp2)
add_math_entrypoint_object(exp2f)
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21 changes: 21 additions & 0 deletions libc/src/math/expf16.h
Original file line number Diff line number Diff line change
@@ -0,0 +1,21 @@
//===-- 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
//
//===----------------------------------------------------------------------===//

#ifndef LLVM_LIBC_SRC_MATH_EXPF16_H
#define LLVM_LIBC_SRC_MATH_EXPF16_H

#include "src/__support/macros/config.h"
#include "src/__support/macros/properties/types.h"

namespace LIBC_NAMESPACE_DECL {

float16 expf16(float16 x);

} // namespace LIBC_NAMESPACE_DECL

#endif // LLVM_LIBC_SRC_MATH_EXPF16_H
21 changes: 21 additions & 0 deletions libc/src/math/generic/CMakeLists.txt
Original file line number Diff line number Diff line change
Expand Up @@ -1226,6 +1226,27 @@ add_entrypoint_object(
-O3
)

add_entrypoint_object(
expf16
SRCS
expf16.cpp
HDRS
../expf16.h
DEPENDS
libc.hdr.errno_macros
libc.hdr.fenv_macros
libc.src.__support.CPP.array
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.nearest_integer
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
COMPILE_OPTIONS
-O3
)

add_entrypoint_object(
exp2
SRCS
Expand Down
173 changes: 173 additions & 0 deletions libc/src/math/generic/expf16.cpp
Original file line number Diff line number Diff line change
@@ -0,0 +1,173 @@
//===-- 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 "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"

namespace LIBC_NAMESPACE_DECL {

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},
}};

// 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,
};

// 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,
};

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()) {
if (auto r = EXPF16_EXCEPTS_LO.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
return r.value();

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);
}
}

if (auto r = EXPF16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
return r.value();

// 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.

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);

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;
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Can we call 1 + x + P a minimax polynomial too, or only P?

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yes, we can, it is for sure minimax with respect to some metric

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);
}

} // namespace LIBC_NAMESPACE_DECL
3 changes: 2 additions & 1 deletion libc/test/UnitTest/FPMatcher.h
Original file line number Diff line number Diff line change
Expand Up @@ -74,7 +74,8 @@ template <typename T> struct FPTest : public Test {
static constexpr T inf = FPBits::inf(Sign::POS).get_val();
static constexpr T neg_inf = FPBits::inf(Sign::NEG).get_val();
static constexpr T min_normal = FPBits::min_normal().get_val();
static constexpr T max_normal = FPBits::max_normal().get_val();
static constexpr T max_normal = FPBits::max_normal(Sign::POS).get_val();
static constexpr T neg_max_normal = FPBits::max_normal(Sign::NEG).get_val();
static constexpr T min_denormal = FPBits::min_subnormal().get_val();
static constexpr T max_denormal = FPBits::max_subnormal().get_val();

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31 changes: 21 additions & 10 deletions libc/test/src/math/CMakeLists.txt
Original file line number Diff line number Diff line change
Expand Up @@ -888,6 +888,19 @@ add_fp_unittest(
libc.src.__support.FPUtil.fp_bits
)

add_fp_unittest(
exp_test
NEED_MPFR
SUITE
libc-math-unittests
SRCS
exp_test.cpp
DEPENDS
libc.src.errno.errno
libc.src.math.exp
libc.src.__support.FPUtil.fp_bits
)

add_fp_unittest(
expf_test
NEED_MPFR
Expand All @@ -902,16 +915,14 @@ add_fp_unittest(
)

add_fp_unittest(
exp_test
NEED_MPFR
SUITE
libc-math-unittests
SRCS
exp_test.cpp
DEPENDS
libc.src.errno.errno
libc.src.math.exp
libc.src.__support.FPUtil.fp_bits
expf16_test
NEED_MPFR
SUITE
libc-math-unittests
SRCS
expf16_test.cpp
DEPENDS
libc.src.math.expf16
)

add_fp_unittest(
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40 changes: 40 additions & 0 deletions libc/test/src/math/expf16_test.cpp
Original file line number Diff line number Diff line change
@@ -0,0 +1,40 @@
//===-- 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
//
//===----------------------------------------------------------------------===//

#include "src/math/expf16.h"
#include "test/UnitTest/FPMatcher.h"
#include "test/UnitTest/Test.h"
#include "utils/MPFRWrapper/MPFRUtils.h"

using LlvmLibcExpf16Test = LIBC_NAMESPACE::testing::FPTest<float16>;

namespace mpfr = LIBC_NAMESPACE::testing::mpfr;

// Range: [0, Inf];
static constexpr uint16_t POS_START = 0x0000U;
static constexpr uint16_t POS_STOP = 0x7c00U;

// Range: [-Inf, 0];
static constexpr uint16_t NEG_START = 0x8000U;
static constexpr uint16_t NEG_STOP = 0xfc00U;

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);
}
}

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);
}
}
11 changes: 11 additions & 0 deletions libc/test/src/math/performance_testing/CMakeLists.txt
Original file line number Diff line number Diff line change
Expand Up @@ -175,6 +175,17 @@ add_perf_binary(
-fno-builtin
)

add_perf_binary(
expf16_perf
SRCS
expf16_perf.cpp
DEPENDS
.single_input_single_output_diff
libc.src.math.expf16
COMPILE_OPTIONS
-fno-builtin
)

add_perf_binary(
fabsf_perf
SRCS
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