1//===----------------------------------------------------------------------===//
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/// \file
10/// Double-precision implementation of exp2f.
11///
12//===----------------------------------------------------------------------===//
13
14#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXP2F_DOUBLE_EVAL_H
15#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP2F_DOUBLE_EVAL_H
16
17#include "src/__support/FPUtil/FEnvImpl.h"
18#include "src/__support/FPUtil/FPBits.h"
19#include "src/__support/FPUtil/PolyEval.h"
20#include "src/__support/FPUtil/except_value_utils.h"
21#include "src/__support/FPUtil/multiply_add.h"
22#include "src/__support/FPUtil/nearest_integer.h"
23#include "src/__support/FPUtil/rounding_mode.h"
24#include "src/__support/common.h"
25#include "src/__support/macros/config.h"
26#include "src/__support/macros/optimization.h"
27#include "src/__support/macros/properties/cpu_features.h"
28#include "src/__support/math/exp10f_utils.h"
29
30namespace LIBC_NAMESPACE_DECL {
31namespace math {
32namespace double_eval {
33
34LIBC_INLINE float exp2f(float x) {
35 using FPBits = fputil::FPBits<float>;
36 FPBits xbits(x);
37
38 uint32_t x_u = xbits.uintval();
39 uint32_t x_abs = x_u & 0x7fff'ffffU;
40
41 // When |x| >= 128, or x is nan, or |x| <= 2^-5
42 if (LIBC_UNLIKELY(x_abs >= 0x4300'0000U || x_abs <= 0x3d00'0000U)) {
43 // |x| <= 2^-5
44 if (x_abs <= 0x3d00'0000) {
45 // |x| < 2^-25
46 if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {
47 return 1.0f + x;
48 }
49
50#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
51 constexpr uint32_t EXVAL1 = 0x3b42'9d37U;
52 constexpr uint32_t EXVAL2 = 0xbcf3'a937U;
53 constexpr uint32_t EXVAL_MASK = EXVAL1 & EXVAL2;
54
55 // Check exceptional values.
56 if (LIBC_UNLIKELY((x_u & EXVAL_MASK) == EXVAL_MASK)) {
57 if (LIBC_UNLIKELY(x_u == EXVAL1)) { // x = 0x1.853a6ep-9f
58 return fputil::round_result_slightly_down(value_rn: 0x1.00870ap+0f);
59 } else if (LIBC_UNLIKELY(x_u == EXVAL2)) { // x = -0x1.e7526ep-6f
60 return fputil::round_result_slightly_down(value_rn: 0x1.f58d62p-1f);
61 }
62 }
63#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
64
65 // Minimax polynomial generated by Sollya with:
66 // > P = fpminimax((2^x - 1)/x, 5, [|D...|], [-2^-5, 2^-5]);
67 constexpr double COEFFS[] = {
68 0x1.62e42fefa39f3p-1, 0x1.ebfbdff82c57bp-3, 0x1.c6b08d6f2d7aap-5,
69 0x1.3b2ab6fc92f5dp-7, 0x1.5d897cfe27125p-10, 0x1.43090e61e6af1p-13};
70 double xd = static_cast<double>(x);
71 double xsq = xd * xd;
72 double c0 = fputil::multiply_add(x: xd, y: COEFFS[1], z: COEFFS[0]);
73 double c1 = fputil::multiply_add(x: xd, y: COEFFS[3], z: COEFFS[2]);
74 double c2 = fputil::multiply_add(x: xd, y: COEFFS[5], z: COEFFS[4]);
75 double p = fputil::polyeval(x: xsq, a0: c0, a: c1, a: c2);
76 double r = fputil::multiply_add(x: p, y: xd, z: 1.0);
77 return static_cast<float>(r);
78 }
79
80 // x >= 128
81 if (xbits.is_pos()) {
82 // x is finite
83 if (x_u < 0x7f80'0000U) {
84#ifndef LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
85 int rounding = fputil::quick_get_round();
86 if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
87 return FPBits::max_normal().get_val();
88#endif // LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
89
90 fputil::set_errno_if_required(ERANGE);
91 fputil::raise_except_if_required(FE_OVERFLOW);
92 }
93 // x is +inf or nan
94 return x + FPBits::inf().get_val();
95 }
96 // x <= -150
97 if (x_u >= 0xc316'0000U) {
98 // exp(-Inf) = 0
99 if (xbits.is_inf())
100 return 0.0f;
101 // exp(nan) = nan
102 if (xbits.is_nan())
103 return x;
104#ifndef LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
105 if (fputil::fenv_is_round_up())
106 return FPBits::min_subnormal().get_val();
107#endif // LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
108 if (x != 0.0f) {
109 fputil::set_errno_if_required(ERANGE);
110 fputil::raise_except_if_required(FE_UNDERFLOW);
111 }
112 return 0.0f;
113 }
114 }
115
116 // For -150 < x < 128, to compute 2^x, we perform the following range
117 // reduction: find hi, mid, lo such that:
118 // x = hi + mid + lo, in which
119 // hi is an integer,
120 // 0 <= mid * 2^5 < 32 is an integer
121 // -2^(-6) <= lo <= 2^-6.
122 // In particular,
123 // hi + mid = round(x * 2^5) * 2^(-5).
124 // Then,
125 // 2^x = 2^(hi + mid + lo) = 2^hi * 2^mid * 2^lo.
126 // 2^mid is stored in the lookup table of 32 elements.
127 // 2^lo is computed using a degree-5 minimax polynomial
128 // generated by Sollya.
129 // We perform 2^hi * 2^mid by simply add hi to the exponent field
130 // of 2^mid.
131
132 // kf = (hi + mid) * 2^5 = round(x * 2^5)
133 float kf = 0;
134 int k = 0;
135#ifdef LIBC_TARGET_CPU_HAS_NEAREST_INT
136 kf = fputil::nearest_integer(x * 32.0f);
137 k = static_cast<int>(kf);
138#else // !LIBC_TARGET_CPU_HAS_NEAREST_INT
139 constexpr float HALF[2] = {0.5f, -0.5f};
140 k = static_cast<int>(fputil::multiply_add(x, y: 32.0f, z: HALF[x < 0.0f]));
141 kf = static_cast<float>(k);
142#endif // LIBC_TARGET_CPU_HAS_NEAREST_INT
143
144 // dx = lo = x - (hi + mid) = x - kf * 2^(-5)
145 double dx = fputil::multiply_add(x: -0x1.0p-5f, y: kf, z: x);
146
147 // hi = floor(kf * 2^(-4))
148 // exp_hi = shift hi to the exponent field of double precision.
149 int64_t exp_hi =
150 static_cast<int64_t>(static_cast<uint64_t>(k >> ExpBase::MID_BITS)
151 << fputil::FPBits<double>::FRACTION_LEN);
152 // mh = 2^hi * 2^mid
153 // mh_bits = bit field of mh
154 int64_t mh_bits = ExpBase::EXP_2_MID[k & ExpBase::MID_MASK] + exp_hi;
155 double mh = fputil::FPBits<double>(uint64_t(mh_bits)).get_val();
156
157 // Degree-5 polynomial approximating (2^x - 1)/x generating by Sollya with:
158 // > P = fpminimax((2^x - 1)/x, 5, [|D...|], [-1/32. 1/32]);
159 constexpr double COEFFS[5] = {0x1.62e42fefa39efp-1, 0x1.ebfbdff8131c4p-3,
160 0x1.c6b08d7061695p-5, 0x1.3b2b1bee74b2ap-7,
161 0x1.5d88091198529p-10};
162 double dx_sq = dx * dx;
163 double c1 = fputil::multiply_add(x: dx, y: COEFFS[0], z: 1.0);
164 double c2 = fputil::multiply_add(x: dx, y: COEFFS[2], z: COEFFS[1]);
165 double c3 = fputil::multiply_add(x: dx, y: COEFFS[4], z: COEFFS[3]);
166 double p = fputil::multiply_add(x: dx_sq, y: c3, z: c2);
167 // 2^x = 2^(hi + mid + lo)
168 // = 2^(hi + mid) * 2^lo
169 // ~ mh * (1 + lo * P(lo))
170 // = mh + (mh*lo) * P(lo)
171 return static_cast<float>(fputil::multiply_add(x: p, y: dx_sq * mh, z: c1 * mh));
172}
173
174} // namespace double_eval
175} // namespace math
176} // namespace LIBC_NAMESPACE_DECL
177
178#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP2F_DOUBLE_EVAL_H
179