xref: /llvm-project/libc/src/math/generic/exp2m1f.cpp (revision 5ff3ff33ff930e4ec49da7910612d8a41eb068cb)
1a8c59750SOverMighty //===-- Implementation of exp2m1f function --------------------------------===//
2a8c59750SOverMighty //
3a8c59750SOverMighty // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4a8c59750SOverMighty // See https://llvm.org/LICENSE.txt for license information.
5a8c59750SOverMighty // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6a8c59750SOverMighty //
7a8c59750SOverMighty //===----------------------------------------------------------------------===//
8a8c59750SOverMighty 
9a8c59750SOverMighty #include "src/math/exp2m1f.h"
10a8c59750SOverMighty #include "src/__support/FPUtil/FEnvImpl.h"
11a8c59750SOverMighty #include "src/__support/FPUtil/FPBits.h"
12a8c59750SOverMighty #include "src/__support/FPUtil/PolyEval.h"
13a8c59750SOverMighty #include "src/__support/FPUtil/except_value_utils.h"
14a8c59750SOverMighty #include "src/__support/FPUtil/multiply_add.h"
15a8c59750SOverMighty #include "src/__support/FPUtil/rounding_mode.h"
16a8c59750SOverMighty #include "src/__support/common.h"
17*5ff3ff33SPetr Hosek #include "src/__support/macros/config.h"
18a8c59750SOverMighty #include "src/__support/macros/optimization.h"
19a8c59750SOverMighty #include "src/__support/macros/properties/cpu_features.h"
20a8c59750SOverMighty #include "src/errno/libc_errno.h"
21a8c59750SOverMighty 
22a8c59750SOverMighty #include "explogxf.h"
23a8c59750SOverMighty 
24*5ff3ff33SPetr Hosek namespace LIBC_NAMESPACE_DECL {
25a8c59750SOverMighty 
26a8c59750SOverMighty static constexpr size_t N_EXCEPTS_LO = 8;
27a8c59750SOverMighty 
28a8c59750SOverMighty static constexpr fputil::ExceptValues<float, N_EXCEPTS_LO> EXP2M1F_EXCEPTS_LO =
29a8c59750SOverMighty     {{
30a8c59750SOverMighty         // (input, RZ output, RU offset, RD offset, RN offset)
31a8c59750SOverMighty         // x = 0x1.36dc8ep-36, exp2m1f(x) = 0x1.aef212p-37 (RZ)
32a8c59750SOverMighty         {0x2d9b'6e47U, 0x2d57'7909U, 1U, 0U, 0U},
33a8c59750SOverMighty         // x = 0x1.224936p-19, exp2m1f(x) = 0x1.926c0ep-20 (RZ)
34a8c59750SOverMighty         {0x3611'249bU, 0x35c9'3607U, 1U, 0U, 1U},
35a8c59750SOverMighty         // x = 0x1.d16d2p-20, exp2m1f(x) = 0x1.429becp-20 (RZ)
36a8c59750SOverMighty         {0x35e8'b690U, 0x35a1'4df6U, 1U, 0U, 1U},
37a8c59750SOverMighty         // x = 0x1.17949ep-14, exp2m1f(x) = 0x1.8397p-15 (RZ)
38a8c59750SOverMighty         {0x388b'ca4fU, 0x3841'cb80U, 1U, 0U, 1U},
39a8c59750SOverMighty         // x = -0x1.9c3e1ep-38, exp2m1f(x) = -0x1.1dbeacp-38 (RZ)
40a8c59750SOverMighty         {0xacce'1f0fU, 0xac8e'df56U, 0U, 1U, 0U},
41a8c59750SOverMighty         // x = -0x1.4d89b4p-32, exp2m1f(x) = -0x1.ce61b6p-33 (RZ)
42a8c59750SOverMighty         {0xafa6'c4daU, 0xaf67'30dbU, 0U, 1U, 1U},
43a8c59750SOverMighty         // x = -0x1.a6eac4p-10, exp2m1f(x) = -0x1.24fadap-10 (RZ)
44a8c59750SOverMighty         {0xbad3'7562U, 0xba92'7d6dU, 0U, 1U, 1U},
45a8c59750SOverMighty         // x = -0x1.e7526ep-6, exp2m1f(x) = -0x1.4e53dep-6 (RZ)
46a8c59750SOverMighty         {0xbcf3'a937U, 0xbca7'29efU, 0U, 1U, 1U},
47a8c59750SOverMighty     }};
48a8c59750SOverMighty 
49a8c59750SOverMighty static constexpr size_t N_EXCEPTS_HI = 3;
50a8c59750SOverMighty 
51a8c59750SOverMighty static constexpr fputil::ExceptValues<float, N_EXCEPTS_HI> EXP2M1F_EXCEPTS_HI =
52a8c59750SOverMighty     {{
53a8c59750SOverMighty         // (input, RZ output, RU offset, RD offset, RN offset)
54a8c59750SOverMighty         // x = 0x1.16a972p-1, exp2m1f(x) = 0x1.d545b2p-2 (RZ)
55a8c59750SOverMighty         {0x3f0b'54b9U, 0x3eea'a2d9U, 1U, 0U, 0U},
56a8c59750SOverMighty         // x = -0x1.9f12acp-5, exp2m1f(x) = -0x1.1ab68cp-5 (RZ)
57a8c59750SOverMighty         {0xbd4f'8956U, 0xbd0d'5b46U, 0U, 1U, 0U},
58a8c59750SOverMighty         // x = -0x1.de7b9cp-5, exp2m1f(x) = -0x1.4508f4p-5 (RZ)
59a8c59750SOverMighty         {0xbd6f'3dceU, 0xbd22'847aU, 0U, 1U, 1U},
60a8c59750SOverMighty     }};
61a8c59750SOverMighty 
62a8c59750SOverMighty LLVM_LIBC_FUNCTION(float, exp2m1f, (float x)) {
63a8c59750SOverMighty   using FPBits = fputil::FPBits<float>;
64a8c59750SOverMighty   FPBits xbits(x);
65a8c59750SOverMighty 
66a8c59750SOverMighty   uint32_t x_u = xbits.uintval();
67a8c59750SOverMighty   uint32_t x_abs = x_u & 0x7fff'ffffU;
68a8c59750SOverMighty 
69a8c59750SOverMighty   // When |x| >= 128, or x is nan, or |x| <= 2^-5
70a8c59750SOverMighty   if (LIBC_UNLIKELY(x_abs >= 0x4300'0000U || x_abs <= 0x3d00'0000U)) {
71a8c59750SOverMighty     // |x| <= 2^-5
72a8c59750SOverMighty     if (x_abs <= 0x3d00'0000U) {
73a8c59750SOverMighty       if (auto r = EXP2M1F_EXCEPTS_LO.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
74a8c59750SOverMighty         return r.value();
75a8c59750SOverMighty 
76a8c59750SOverMighty       // Minimax polynomial generated by Sollya with:
77a8c59750SOverMighty       // > display = hexadecimal;
78a8c59750SOverMighty       // > fpminimax((2^x - 1)/x, 5, [|D...|], [-2^-5, 2^-5]);
79a8c59750SOverMighty       constexpr double COEFFS[] = {
80a8c59750SOverMighty           0x1.62e42fefa39f3p-1, 0x1.ebfbdff82c57bp-3,  0x1.c6b08d6f2d7aap-5,
81a8c59750SOverMighty           0x1.3b2ab6fc92f5dp-7, 0x1.5d897cfe27125p-10, 0x1.43090e61e6af1p-13};
82a8c59750SOverMighty       double xd = x;
83a8c59750SOverMighty       double xsq = xd * xd;
84a8c59750SOverMighty       double c0 = fputil::multiply_add(xd, COEFFS[1], COEFFS[0]);
85a8c59750SOverMighty       double c1 = fputil::multiply_add(xd, COEFFS[3], COEFFS[2]);
86a8c59750SOverMighty       double c2 = fputil::multiply_add(xd, COEFFS[5], COEFFS[4]);
87a8c59750SOverMighty       double p = fputil::polyeval(xsq, c0, c1, c2);
88a8c59750SOverMighty       return static_cast<float>(p * xd);
89a8c59750SOverMighty     }
90a8c59750SOverMighty 
91a8c59750SOverMighty     // x >= 128, or x is nan
92a8c59750SOverMighty     if (xbits.is_pos()) {
93a8c59750SOverMighty       if (xbits.is_finite()) {
94a8c59750SOverMighty         int rounding = fputil::quick_get_round();
95a8c59750SOverMighty         if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
96a8c59750SOverMighty           return FPBits::max_normal().get_val();
97a8c59750SOverMighty 
98a8c59750SOverMighty         fputil::set_errno_if_required(ERANGE);
99a8c59750SOverMighty         fputil::raise_except_if_required(FE_OVERFLOW);
100a8c59750SOverMighty       }
101a8c59750SOverMighty 
102a8c59750SOverMighty       // x >= 128 and 2^x - 1 rounds to +inf, or x is +inf or nan
103a8c59750SOverMighty       return x + FPBits::inf().get_val();
104a8c59750SOverMighty     }
105a8c59750SOverMighty   }
106a8c59750SOverMighty 
107a8c59750SOverMighty   if (LIBC_UNLIKELY(x <= -25.0f)) {
108a8c59750SOverMighty     // 2^(-inf) - 1 = -1
109a8c59750SOverMighty     if (xbits.is_inf())
110a8c59750SOverMighty       return -1.0f;
111a8c59750SOverMighty     // 2^nan - 1 = nan
112a8c59750SOverMighty     if (xbits.is_nan())
113a8c59750SOverMighty       return x;
114a8c59750SOverMighty 
115a8c59750SOverMighty     int rounding = fputil::quick_get_round();
116a8c59750SOverMighty     if (rounding == FE_UPWARD || rounding == FE_TOWARDZERO)
117a8c59750SOverMighty       return -0x1.ffff'fep-1f; // -1.0f + 0x1.0p-24f
118a8c59750SOverMighty 
119a8c59750SOverMighty     fputil::set_errno_if_required(ERANGE);
120a8c59750SOverMighty     fputil::raise_except_if_required(FE_UNDERFLOW);
121a8c59750SOverMighty     return -1.0f;
122a8c59750SOverMighty   }
123a8c59750SOverMighty 
124a8c59750SOverMighty   if (auto r = EXP2M1F_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
125a8c59750SOverMighty     return r.value();
126a8c59750SOverMighty 
127a8c59750SOverMighty   // For -25 < x < 128, to compute 2^x, we perform the following range
128a8c59750SOverMighty   // reduction: find hi, mid, lo such that:
129a8c59750SOverMighty   //   x = hi + mid + lo, in which:
130a8c59750SOverMighty   //     hi is an integer,
131a8c59750SOverMighty   //     0 <= mid * 2^5 < 32 is an integer,
132a8c59750SOverMighty   //     -2^(-6) <= lo <= 2^(-6).
133a8c59750SOverMighty   // In particular,
134a8c59750SOverMighty   //   hi + mid = round(x * 2^5) * 2^(-5).
135a8c59750SOverMighty   // Then,
136a8c59750SOverMighty   //   2^x = 2^(hi + mid + lo) = 2^hi * 2^mid * 2^lo.
137a8c59750SOverMighty   // 2^mid is stored in the lookup table of 32 elements.
138a8c59750SOverMighty   // 2^lo is computed using a degree-4 minimax polynomial generated by Sollya.
139a8c59750SOverMighty   // We perform 2^hi * 2^mid by simply add hi to the exponent field of 2^mid.
140a8c59750SOverMighty 
141a8c59750SOverMighty   // kf = (hi + mid) * 2^5 = round(x * 2^5)
142a8c59750SOverMighty   float kf;
143a8c59750SOverMighty   int k;
144a8c59750SOverMighty #ifdef LIBC_TARGET_CPU_HAS_NEAREST_INT
145a8c59750SOverMighty   kf = fputil::nearest_integer(x * 32.0f);
146a8c59750SOverMighty   k = static_cast<int>(kf);
147a8c59750SOverMighty #else
148a8c59750SOverMighty   constexpr float HALF[2] = {0.5f, -0.5f};
149a8c59750SOverMighty   k = static_cast<int>(fputil::multiply_add(x, 32.0f, HALF[x < 0.0f]));
150a8c59750SOverMighty   kf = static_cast<float>(k);
151a8c59750SOverMighty #endif // LIBC_TARGET_CPU_HAS_NEAREST_INT
152a8c59750SOverMighty 
153a8c59750SOverMighty   // lo = x - (hi + mid) = x - kf * 2^(-5)
154a8c59750SOverMighty   double lo = fputil::multiply_add(-0x1.0p-5f, kf, x);
155a8c59750SOverMighty 
156a8c59750SOverMighty   // hi = floor(kf * 2^(-4))
157a8c59750SOverMighty   // exp2_hi = shift hi to the exponent field of double precision.
158a8c59750SOverMighty   int64_t exp2_hi =
159a8c59750SOverMighty       static_cast<int64_t>(static_cast<uint64_t>(k >> ExpBase::MID_BITS)
160a8c59750SOverMighty                            << fputil::FPBits<double>::FRACTION_LEN);
161a8c59750SOverMighty   // mh = 2^hi * 2^mid
162a8c59750SOverMighty   // mh_bits = bit field of mh
163a8c59750SOverMighty   int64_t mh_bits = ExpBase::EXP_2_MID[k & ExpBase::MID_MASK] + exp2_hi;
164a8c59750SOverMighty   double mh = fputil::FPBits<double>(static_cast<uint64_t>(mh_bits)).get_val();
165a8c59750SOverMighty 
166a8c59750SOverMighty   // Degree-4 polynomial approximating (2^x - 1)/x generated by Sollya with:
167a8c59750SOverMighty   // > display = hexadecimal;
168a8c59750SOverMighty   // > fpminimax((2^x - 1)/x, 4, [|D...|], [-2^-6, 2^-6]);
169a8c59750SOverMighty   constexpr double COEFFS[5] = {0x1.62e42fefa39efp-1, 0x1.ebfbdff8131c4p-3,
170a8c59750SOverMighty                                 0x1.c6b08d7061695p-5, 0x1.3b2b1bee74b2ap-7,
171a8c59750SOverMighty                                 0x1.5d88091198529p-10};
172a8c59750SOverMighty   double lo_sq = lo * lo;
173a8c59750SOverMighty   double c1 = fputil::multiply_add(lo, COEFFS[0], 1.0);
174a8c59750SOverMighty   double c2 = fputil::multiply_add(lo, COEFFS[2], COEFFS[1]);
175a8c59750SOverMighty   double c3 = fputil::multiply_add(lo, COEFFS[4], COEFFS[3]);
176a8c59750SOverMighty   double exp2_lo = fputil::polyeval(lo_sq, c1, c2, c3);
177a8c59750SOverMighty   // 2^x - 1 = 2^(hi + mid + lo) - 1
178a8c59750SOverMighty   //         = 2^(hi + mid) * 2^lo - 1
179a8c59750SOverMighty   //         ~ mh * (1 + lo * P(lo)) - 1
180a8c59750SOverMighty   //         = mh * exp2_lo - 1
181a8c59750SOverMighty   return static_cast<float>(fputil::multiply_add(exp2_lo, mh, -1.0));
182a8c59750SOverMighty }
183a8c59750SOverMighty 
184*5ff3ff33SPetr Hosek } // namespace LIBC_NAMESPACE_DECL
185