1 //===-- Single-precision log1p(x) function --------------------------------===//
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 #include "src/math/log1pf.h"
10 #include "common_constants.h" // Lookup table for (1/f) and log(f)
11 #include "src/__support/FPUtil/FEnvImpl.h"
12 #include "src/__support/FPUtil/FMA.h"
13 #include "src/__support/FPUtil/FPBits.h"
14 #include "src/__support/FPUtil/PolyEval.h"
15 #include "src/__support/FPUtil/except_value_utils.h"
16 #include "src/__support/FPUtil/multiply_add.h"
17 #include "src/__support/common.h"
18 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
19 #include "src/__support/macros/properties/cpu_features.h"
20
21 // This is an algorithm for log10(x) in single precision which is
22 // correctly rounded for all rounding modes.
23 // - An exhaustive test show that when x >= 2^45, log1pf(x) == logf(x)
24 // for all rounding modes.
25 // - When 2^(-6) <= |x| < 2^45, the sum (double(x) + 1.0) is exact,
26 // so we can adapt the correctly rounded algorithm of logf to compute
27 // log(double(x) + 1.0) correctly. For more information about the logf
28 // algorithm, see `libc/src/math/generic/logf.cpp`.
29 // - When |x| < 2^(-6), we use a degree-8 polynomial in double precision
30 // generated with Sollya using the following command:
31 // fpminimax(log(1 + x)/x, 7, [|D...|], [-2^-6; 2^-6]);
32
33 namespace LIBC_NAMESPACE {
34
35 namespace internal {
36
37 // We don't need to treat denormal and 0
log(double x)38 LIBC_INLINE float log(double x) {
39 constexpr double LOG_2 = 0x1.62e42fefa39efp-1;
40
41 using FPBits = typename fputil::FPBits<double>;
42 FPBits xbits(x);
43
44 uint64_t x_u = xbits.uintval();
45
46 if (LIBC_UNLIKELY(x_u > FPBits::max_normal().uintval())) {
47 if (xbits.is_neg() && !xbits.is_nan()) {
48 fputil::set_errno_if_required(EDOM);
49 fputil::raise_except_if_required(FE_INVALID);
50 return fputil::FPBits<float>::quiet_nan().get_val();
51 }
52 return static_cast<float>(x);
53 }
54
55 double m = static_cast<double>(xbits.get_exponent());
56
57 // Get the 8 highest bits, use 7 bits (excluding the implicit hidden bit) for
58 // lookup tables.
59 int f_index = static_cast<int>(xbits.get_mantissa() >>
60 (fputil::FPBits<double>::FRACTION_LEN - 7));
61
62 // Set bits to 1.m
63 xbits.set_biased_exponent(0x3FF);
64 FPBits f = xbits;
65
66 // Clear the lowest 45 bits.
67 f.set_uintval(f.uintval() & ~0x0000'1FFF'FFFF'FFFFULL);
68
69 double d = xbits.get_val() - f.get_val();
70 d *= ONE_OVER_F[f_index];
71
72 double extra_factor = fputil::multiply_add(m, LOG_2, LOG_F[f_index]);
73
74 double r = fputil::polyeval(d, extra_factor, 0x1.fffffffffffacp-1,
75 -0x1.fffffffef9cb2p-2, 0x1.5555513bc679ap-2,
76 -0x1.fff4805ea441p-3, 0x1.930180dbde91ap-3);
77
78 return static_cast<float>(r);
79 }
80
81 } // namespace internal
82
83 LLVM_LIBC_FUNCTION(float, log1pf, (float x)) {
84 using FPBits = typename fputil::FPBits<float>;
85 FPBits xbits(x);
86 uint32_t x_u = xbits.uintval();
87 uint32_t x_a = x_u & 0x7fff'ffffU;
88 double xd = static_cast<double>(x);
89
90 // Use log1p(x) = log(1 + x) for |x| > 2^-6;
91 if (x_a > 0x3c80'0000U) {
92 // Hard-to-round cases.
93 switch (x_u) {
94 case 0x41078febU: // x = 0x1.0f1fd6p3
95 return fputil::round_result_slightly_up(0x1.1fcbcep1f);
96 case 0x5cd69e88U: // x = 0x1.ad3d1p+58f
97 return fputil::round_result_slightly_up(0x1.45c146p+5f);
98 case 0x65d890d3U: // x = 0x1.b121a6p+76f
99 return fputil::round_result_slightly_down(0x1.a9a3f2p+5f);
100 case 0x6f31a8ecU: // x = 0x1.6351d8p+95f
101 return fputil::round_result_slightly_down(0x1.08b512p+6f);
102 case 0x7a17f30aU: // x = 0x1.2fe614p+117f
103 return fputil::round_result_slightly_up(0x1.451436p+6f);
104 case 0xbd1d20afU: // x = -0x1.3a415ep-5f
105 return fputil::round_result_slightly_up(-0x1.407112p-5f);
106 case 0xbf800000U: // x = -1.0
107 fputil::set_errno_if_required(ERANGE);
108 fputil::raise_except_if_required(FE_DIVBYZERO);
109 return FPBits::inf(Sign::NEG).get_val();
110 #ifndef LIBC_TARGET_CPU_HAS_FMA
111 case 0x4cc1c80bU: // x = 0x1.839016p+26f
112 return fputil::round_result_slightly_down(0x1.26fc04p+4f);
113 case 0x5ee8984eU: // x = 0x1.d1309cp+62f
114 return fputil::round_result_slightly_up(0x1.5c9442p+5f);
115 case 0x665e7ca6U: // x = 0x1.bcf94cp+77f
116 return fputil::round_result_slightly_up(0x1.af66cp+5f);
117 case 0x79e7ec37U: // x = 0x1.cfd86ep+116f
118 return fputil::round_result_slightly_up(0x1.43ff6ep+6f);
119 #endif // LIBC_TARGET_CPU_HAS_FMA
120 }
121
122 return internal::log(xd + 1.0);
123 }
124
125 // |x| <= 2^-6.
126 // Hard-to round cases.
127 switch (x_u) {
128 case 0x35400003U: // x = 0x1.800006p-21f
129 return fputil::round_result_slightly_down(0x1.7ffffep-21f);
130 case 0x3710001bU: // x = 0x1.200036p-17f
131 return fputil::round_result_slightly_down(0x1.1fffe6p-17f);
132 case 0xb53ffffdU: // x = -0x1.7ffffap-21
133 return fputil::round_result_slightly_down(-0x1.800002p-21f);
134 case 0xb70fffe5U: // x = -0x1.1fffcap-17
135 return fputil::round_result_slightly_down(-0x1.20001ap-17f);
136 case 0xbb0ec8c4U: // x = -0x1.1d9188p-9
137 return fputil::round_result_slightly_up(-0x1.1de14ap-9f);
138 }
139
140 // Polymial generated by Sollya with:
141 // > fpminimax(log(1 + x)/x, 7, [|D...|], [-2^-6; 2^-6]);
142 const double COEFFS[7] = {-0x1.0000000000000p-1, 0x1.5555555556aadp-2,
143 -0x1.000000000181ap-2, 0x1.999998998124ep-3,
144 -0x1.55555452e2a2bp-3, 0x1.24adb8cde4aa7p-3,
145 -0x1.0019db915ef6fp-3};
146
147 double xsq = xd * xd;
148 double c0 = fputil::multiply_add(xd, COEFFS[1], COEFFS[0]);
149 double c1 = fputil::multiply_add(xd, COEFFS[3], COEFFS[2]);
150 double c2 = fputil::multiply_add(xd, COEFFS[5], COEFFS[4]);
151 double r = fputil::polyeval(xsq, xd, c0, c1, c2, COEFFS[6]);
152
153 return static_cast<float>(r);
154 }
155
156 } // namespace LIBC_NAMESPACE
157