Skip to content

Commit a55c4c8

Browse files
bassiounixbassiounix
authored
[libc][math] Refactor exp2m1f implementation to header-only in src/__support/math folder. (#162017)
Part of #147386 in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
1 parent 212eb81 commit a55c4c8

File tree

9 files changed

+259
-188
lines changed

9 files changed

+259
-188
lines changed

‎libc/shared/math.h‎

Lines changed: 1 addition & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -50,6 +50,7 @@
5050
#include "math/exp2.h"
5151
#include "math/exp2f.h"
5252
#include "math/exp2f16.h"
53+
#include "math/exp2m1f.h"
5354
#include "math/expf.h"
5455
#include "math/expf16.h"
5556
#include "math/frexpf.h"

‎libc/shared/math/exp2m1f.h‎

Lines changed: 23 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,23 @@
1+
//===-- Shared exp2m1f function ---------------------------------*- C++ -*-===//
2+
//
3+
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4+
// See https://llvm.org/LICENSE.txt for license information.
5+
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6+
//
7+
//===----------------------------------------------------------------------===//
8+
9+
#ifndef LLVM_LIBC_SHARED_MATH_EXP2M1F_H
10+
#define LLVM_LIBC_SHARED_MATH_EXP2M1F_H
11+
12+
#include "shared/libc_common.h"
13+
#include "src/__support/math/exp2m1f.h"
14+
15+
namespace LIBC_NAMESPACE_DECL {
16+
namespace shared {
17+
18+
using math::exp2m1f;
19+
20+
} // namespace shared
21+
} // namespace LIBC_NAMESPACE_DECL
22+
23+
#endif // LLVM_LIBC_SHARED_MATH_EXP2M1F_H

‎libc/src/__support/math/CMakeLists.txt‎

Lines changed: 18 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -751,6 +751,24 @@ add_header_library(
751751
libc.src.__support.macros.optimization
752752
)
753753

754+
add_header_library(
755+
exp2m1f
756+
HDRS
757+
exp2m1f.h
758+
DEPENDS
759+
.exp10f_utils
760+
libc.src.errno.errno
761+
libc.src.__support.common
762+
libc.src.__support.FPUtil.except_value_utils
763+
libc.src.__support.FPUtil.fenv_impl
764+
libc.src.__support.FPUtil.fp_bits
765+
libc.src.__support.FPUtil.multiply_add
766+
libc.src.__support.FPUtil.polyeval
767+
libc.src.__support.FPUtil.rounding_mode
768+
libc.src.__support.macros.optimization
769+
libc.src.__support.macros.properties.cpu_features
770+
)
771+
754772
add_header_library(
755773
exp10
756774
HDRS

‎libc/src/__support/math/exp2m1f.h‎

Lines changed: 195 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,195 @@
1+
//===-- Implementation header for exp2m1f ------------------------*- C++-*-===//
2+
//
3+
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4+
// See https://llvm.org/LICENSE.txt for license information.
5+
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6+
//
7+
//===----------------------------------------------------------------------===//
8+
9+
#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXP2M1F_H
10+
#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP2M1F_H
11+
12+
#include "exp10f_utils.h"
13+
#include "src/__support/FPUtil/FEnvImpl.h"
14+
#include "src/__support/FPUtil/FPBits.h"
15+
#include "src/__support/FPUtil/PolyEval.h"
16+
#include "src/__support/FPUtil/except_value_utils.h"
17+
#include "src/__support/FPUtil/multiply_add.h"
18+
#include "src/__support/FPUtil/rounding_mode.h"
19+
#include "src/__support/common.h"
20+
#include "src/__support/libc_errno.h"
21+
#include "src/__support/macros/config.h"
22+
#include "src/__support/macros/optimization.h"
23+
#include "src/__support/macros/properties/cpu_features.h"
24+
25+
namespace LIBC_NAMESPACE_DECL {
26+
27+
namespace math {
28+
29+
LIBC_INLINE static constexpr float exp2m1f(float x) {
30+
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
31+
constexpr size_t N_EXCEPTS_LO = 8;
32+
33+
constexpr fputil::ExceptValues<float, N_EXCEPTS_LO> EXP2M1F_EXCEPTS_LO = {{
34+
// (input, RZ output, RU offset, RD offset, RN offset)
35+
// x = 0x1.36dc8ep-36, exp2m1f(x) = 0x1.aef212p-37 (RZ)
36+
{0x2d9b'6e47U, 0x2d57'7909U, 1U, 0U, 0U},
37+
// x = 0x1.224936p-19, exp2m1f(x) = 0x1.926c0ep-20 (RZ)
38+
{0x3611'249bU, 0x35c9'3607U, 1U, 0U, 1U},
39+
// x = 0x1.d16d2p-20, exp2m1f(x) = 0x1.429becp-20 (RZ)
40+
{0x35e8'b690U, 0x35a1'4df6U, 1U, 0U, 1U},
41+
// x = 0x1.17949ep-14, exp2m1f(x) = 0x1.8397p-15 (RZ)
42+
{0x388b'ca4fU, 0x3841'cb80U, 1U, 0U, 1U},
43+
// x = -0x1.9c3e1ep-38, exp2m1f(x) = -0x1.1dbeacp-38 (RZ)
44+
{0xacce'1f0fU, 0xac8e'df56U, 0U, 1U, 0U},
45+
// x = -0x1.4d89b4p-32, exp2m1f(x) = -0x1.ce61b6p-33 (RZ)
46+
{0xafa6'c4daU, 0xaf67'30dbU, 0U, 1U, 1U},
47+
// x = -0x1.a6eac4p-10, exp2m1f(x) = -0x1.24fadap-10 (RZ)
48+
{0xbad3'7562U, 0xba92'7d6dU, 0U, 1U, 1U},
49+
// x = -0x1.e7526ep-6, exp2m1f(x) = -0x1.4e53dep-6 (RZ)
50+
{0xbcf3'a937U, 0xbca7'29efU, 0U, 1U, 1U},
51+
}};
52+
53+
constexpr size_t N_EXCEPTS_HI = 3;
54+
55+
constexpr fputil::ExceptValues<float, N_EXCEPTS_HI> EXP2M1F_EXCEPTS_HI = {{
56+
// (input, RZ output, RU offset, RD offset, RN offset)
57+
// x = 0x1.16a972p-1, exp2m1f(x) = 0x1.d545b2p-2 (RZ)
58+
{0x3f0b'54b9U, 0x3eea'a2d9U, 1U, 0U, 0U},
59+
// x = -0x1.9f12acp-5, exp2m1f(x) = -0x1.1ab68cp-5 (RZ)
60+
{0xbd4f'8956U, 0xbd0d'5b46U, 0U, 1U, 0U},
61+
// x = -0x1.de7b9cp-5, exp2m1f(x) = -0x1.4508f4p-5 (RZ)
62+
{0xbd6f'3dceU, 0xbd22'847aU, 0U, 1U, 1U},
63+
}};
64+
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
65+
66+
using FPBits = fputil::FPBits<float>;
67+
FPBits xbits(x);
68+
69+
uint32_t x_u = xbits.uintval();
70+
uint32_t x_abs = x_u & 0x7fff'ffffU;
71+
72+
// When |x| >= 128, or x is nan, or |x| <= 2^-5
73+
if (LIBC_UNLIKELY(x_abs >= 0x4300'0000U || x_abs <= 0x3d00'0000U)) {
74+
// |x| <= 2^-5
75+
if (x_abs <= 0x3d00'0000U) {
76+
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
77+
if (auto r = EXP2M1F_EXCEPTS_LO.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
78+
return r.value();
79+
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
80+
81+
// Minimax polynomial generated by Sollya with:
82+
// > display = hexadecimal;
83+
// > fpminimax((2^x - 1)/x, 5, [|D...|], [-2^-5, 2^-5]);
84+
constexpr double COEFFS[] = {
85+
0x1.62e42fefa39f3p-1, 0x1.ebfbdff82c57bp-3, 0x1.c6b08d6f2d7aap-5,
86+
0x1.3b2ab6fc92f5dp-7, 0x1.5d897cfe27125p-10, 0x1.43090e61e6af1p-13};
87+
double xd = x;
88+
double xsq = xd * xd;
89+
double c0 = fputil::multiply_add(xd, COEFFS[1], COEFFS[0]);
90+
double c1 = fputil::multiply_add(xd, COEFFS[3], COEFFS[2]);
91+
double c2 = fputil::multiply_add(xd, COEFFS[5], COEFFS[4]);
92+
double p = fputil::polyeval(xsq, c0, c1, c2);
93+
return static_cast<float>(p * xd);
94+
}
95+
96+
// x >= 128, or x is nan
97+
if (xbits.is_pos()) {
98+
if (xbits.is_finite()) {
99+
int rounding = fputil::quick_get_round();
100+
if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
101+
return FPBits::max_normal().get_val();
102+
103+
fputil::set_errno_if_required(ERANGE);
104+
fputil::raise_except_if_required(FE_OVERFLOW);
105+
}
106+
107+
// x >= 128 and 2^x - 1 rounds to +inf, or x is +inf or nan
108+
return x + FPBits::inf().get_val();
109+
}
110+
}
111+
112+
if (LIBC_UNLIKELY(x <= -25.0f)) {
113+
// 2^(-inf) - 1 = -1
114+
if (xbits.is_inf())
115+
return -1.0f;
116+
// 2^nan - 1 = nan
117+
if (xbits.is_nan())
118+
return x;
119+
120+
int rounding = fputil::quick_get_round();
121+
if (rounding == FE_UPWARD || rounding == FE_TOWARDZERO)
122+
return -0x1.ffff'fep-1f; // -1.0f + 0x1.0p-24f
123+
124+
fputil::set_errno_if_required(ERANGE);
125+
fputil::raise_except_if_required(FE_UNDERFLOW);
126+
return -1.0f;
127+
}
128+
129+
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
130+
if (auto r = EXP2M1F_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
131+
return r.value();
132+
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
133+
134+
// For -25 < x < 128, to compute 2^x, we perform the following range
135+
// reduction: find hi, mid, lo such that:
136+
// x = hi + mid + lo, in which:
137+
// hi is an integer,
138+
// 0 <= mid * 2^5 < 32 is an integer,
139+
// -2^(-6) <= lo <= 2^(-6).
140+
// In particular,
141+
// hi + mid = round(x * 2^5) * 2^(-5).
142+
// Then,
143+
// 2^x = 2^(hi + mid + lo) = 2^hi * 2^mid * 2^lo.
144+
// 2^mid is stored in the lookup table of 32 elements.
145+
// 2^lo is computed using a degree-4 minimax polynomial generated by Sollya.
146+
// We perform 2^hi * 2^mid by simply add hi to the exponent field of 2^mid.
147+
148+
// kf = (hi + mid) * 2^5 = round(x * 2^5)
149+
float kf = 0;
150+
int k = 0;
151+
#ifdef LIBC_TARGET_CPU_HAS_NEAREST_INT
152+
kf = fputil::nearest_integer(x * 32.0f);
153+
k = static_cast<int>(kf);
154+
#else
155+
constexpr float HALF[2] = {0.5f, -0.5f};
156+
k = static_cast<int>(fputil::multiply_add(x, 32.0f, HALF[x < 0.0f]));
157+
kf = static_cast<float>(k);
158+
#endif // LIBC_TARGET_CPU_HAS_NEAREST_INT
159+
160+
// lo = x - (hi + mid) = x - kf * 2^(-5)
161+
double lo = fputil::multiply_add(-0x1.0p-5f, kf, x);
162+
163+
// hi = floor(kf * 2^(-4))
164+
// exp2_hi = shift hi to the exponent field of double precision.
165+
int64_t exp2_hi =
166+
static_cast<int64_t>(static_cast<uint64_t>(k >> ExpBase::MID_BITS)
167+
<< fputil::FPBits<double>::FRACTION_LEN);
168+
// mh = 2^hi * 2^mid
169+
// mh_bits = bit field of mh
170+
int64_t mh_bits = ExpBase::EXP_2_MID[k & ExpBase::MID_MASK] + exp2_hi;
171+
double mh = fputil::FPBits<double>(static_cast<uint64_t>(mh_bits)).get_val();
172+
173+
// Degree-4 polynomial approximating (2^x - 1)/x generated by Sollya with:
174+
// > display = hexadecimal;
175+
// > fpminimax((2^x - 1)/x, 4, [|D...|], [-2^-6, 2^-6]);
176+
constexpr double COEFFS[5] = {0x1.62e42fefa39efp-1, 0x1.ebfbdff8131c4p-3,
177+
0x1.c6b08d7061695p-5, 0x1.3b2b1bee74b2ap-7,
178+
0x1.5d88091198529p-10};
179+
double lo_sq = lo * lo;
180+
double c1 = fputil::multiply_add(lo, COEFFS[0], 1.0);
181+
double c2 = fputil::multiply_add(lo, COEFFS[2], COEFFS[1]);
182+
double c3 = fputil::multiply_add(lo, COEFFS[4], COEFFS[3]);
183+
double exp2_lo = fputil::polyeval(lo_sq, c1, c2, c3);
184+
// 2^x - 1 = 2^(hi + mid + lo) - 1
185+
// = 2^(hi + mid) * 2^lo - 1
186+
// ~ mh * (1 + lo * P(lo)) - 1
187+
// = mh * exp2_lo - 1
188+
return static_cast<float>(fputil::multiply_add(exp2_lo, mh, -1.0));
189+
}
190+
191+
} // namespace math
192+
193+
} // namespace LIBC_NAMESPACE_DECL
194+
195+
#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP2M1F_H

‎libc/src/math/generic/CMakeLists.txt‎

Lines changed: 1 addition & 11 deletions
Original file line numberDiff line numberDiff line change
@@ -1488,17 +1488,7 @@ add_entrypoint_object(
14881488
HDRS
14891489
../exp2m1f.h
14901490
DEPENDS
1491-
libc.src.errno.errno
1492-
libc.src.__support.common
1493-
libc.src.__support.FPUtil.except_value_utils
1494-
libc.src.__support.FPUtil.fenv_impl
1495-
libc.src.__support.FPUtil.fp_bits
1496-
libc.src.__support.FPUtil.multiply_add
1497-
libc.src.__support.FPUtil.polyeval
1498-
libc.src.__support.FPUtil.rounding_mode
1499-
libc.src.__support.macros.optimization
1500-
libc.src.__support.macros.properties.cpu_features
1501-
libc.src.__support.math.exp10f_utils
1491+
libc.src.__support.math.exp2m1f
15021492
)
15031493

15041494
add_entrypoint_object(

0 commit comments

Comments
 (0)