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/config.h"
19 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
20 #include "src/__support/macros/properties/cpu_features.h"
21
22 // This is an algorithm for log10(x) in single precision which is
23 // correctly rounded for all rounding modes.
24 // - An exhaustive test show that when x >= 2^45, log1pf(x) == logf(x)
25 // for all rounding modes.
26 // - When 2^(-6) <= |x| < 2^45, the sum (double(x) + 1.0) is exact,
27 // so we can adapt the correctly rounded algorithm of logf to compute
28 // log(double(x) + 1.0) correctly. For more information about the logf
29 // algorithm, see `libc/src/math/generic/logf.cpp`.
30 // - When |x| < 2^(-6), we use a degree-8 polynomial in double precision
31 // generated with Sollya using the following command:
32 // fpminimax(log(1 + x)/x, 7, [|D...|], [-2^-6; 2^-6]);
33
34 namespace LIBC_NAMESPACE_DECL {
35
36 namespace internal {
37
38 // We don't need to treat denormal and 0
log(double x)39 LIBC_INLINE float log(double x) {
40 constexpr double LOG_2 = 0x1.62e42fefa39efp-1;
41
42 using FPBits = typename fputil::FPBits<double>;
43 FPBits xbits(x);
44
45 uint64_t x_u = xbits.uintval();
46
47 if (LIBC_UNLIKELY(x_u > FPBits::max_normal().uintval())) {
48 if (xbits.is_neg() && !xbits.is_nan()) {
49 fputil::set_errno_if_required(EDOM);
50 fputil::raise_except_if_required(FE_INVALID);
51 return fputil::FPBits<float>::quiet_nan().get_val();
52 }
53 return static_cast<float>(x);
54 }
55
56 double m = static_cast<double>(xbits.get_exponent());
57
58 // Get the 8 highest bits, use 7 bits (excluding the implicit hidden bit) for
59 // lookup tables.
60 int f_index = static_cast<int>(xbits.get_mantissa() >>
61 (fputil::FPBits<double>::FRACTION_LEN - 7));
62
63 // Set bits to 1.m
64 xbits.set_biased_exponent(0x3FF);
65 FPBits f = xbits;
66
67 // Clear the lowest 45 bits.
68 f.set_uintval(f.uintval() & ~0x0000'1FFF'FFFF'FFFFULL);
69
70 double d = xbits.get_val() - f.get_val();
71 d *= ONE_OVER_F[f_index];
72
73 double extra_factor = fputil::multiply_add(m, LOG_2, LOG_F[f_index]);
74
75 double r = fputil::polyeval(d, extra_factor, 0x1.fffffffffffacp-1,
76 -0x1.fffffffef9cb2p-2, 0x1.5555513bc679ap-2,
77 -0x1.fff4805ea441p-3, 0x1.930180dbde91ap-3);
78
79 return static_cast<float>(r);
80 }
81
82 } // namespace internal
83
84 LLVM_LIBC_FUNCTION(float, log1pf, (float x)) {
85 using FPBits = typename fputil::FPBits<float>;
86 FPBits xbits(x);
87 uint32_t x_u = xbits.uintval();
88 uint32_t x_a = x_u & 0x7fff'ffffU;
89 double xd = static_cast<double>(x);
90
91 // Use log1p(x) = log(1 + x) for |x| > 2^-6;
92 if (x_a > 0x3c80'0000U) {
93 // Hard-to-round cases.
94 switch (x_u) {
95 case 0x41078febU: // x = 0x1.0f1fd6p3
96 return fputil::round_result_slightly_up(0x1.1fcbcep1f);
97 case 0x5cd69e88U: // x = 0x1.ad3d1p+58f
98 return fputil::round_result_slightly_up(0x1.45c146p+5f);
99 case 0x65d890d3U: // x = 0x1.b121a6p+76f
100 return fputil::round_result_slightly_down(0x1.a9a3f2p+5f);
101 case 0x6f31a8ecU: // x = 0x1.6351d8p+95f
102 return fputil::round_result_slightly_down(0x1.08b512p+6f);
103 case 0x7a17f30aU: // x = 0x1.2fe614p+117f
104 return fputil::round_result_slightly_up(0x1.451436p+6f);
105 case 0xbd1d20afU: // x = -0x1.3a415ep-5f
106 return fputil::round_result_slightly_up(-0x1.407112p-5f);
107 case 0xbf800000U: // x = -1.0
108 fputil::set_errno_if_required(ERANGE);
109 fputil::raise_except_if_required(FE_DIVBYZERO);
110 return FPBits::inf(Sign::NEG).get_val();
111 #ifndef LIBC_TARGET_CPU_HAS_FMA
112 case 0x4cc1c80bU: // x = 0x1.839016p+26f
113 return fputil::round_result_slightly_down(0x1.26fc04p+4f);
114 case 0x5ee8984eU: // x = 0x1.d1309cp+62f
115 return fputil::round_result_slightly_up(0x1.5c9442p+5f);
116 case 0x665e7ca6U: // x = 0x1.bcf94cp+77f
117 return fputil::round_result_slightly_up(0x1.af66cp+5f);
118 case 0x79e7ec37U: // x = 0x1.cfd86ep+116f
119 return fputil::round_result_slightly_up(0x1.43ff6ep+6f);
120 #endif // LIBC_TARGET_CPU_HAS_FMA
121 }
122
123 return internal::log(xd + 1.0);
124 }
125
126 // |x| <= 2^-6.
127 // Hard-to round cases.
128 switch (x_u) {
129 case 0x35400003U: // x = 0x1.800006p-21f
130 return fputil::round_result_slightly_down(0x1.7ffffep-21f);
131 case 0x3710001bU: // x = 0x1.200036p-17f
132 return fputil::round_result_slightly_down(0x1.1fffe6p-17f);
133 case 0xb53ffffdU: // x = -0x1.7ffffap-21
134 return fputil::round_result_slightly_down(-0x1.800002p-21f);
135 case 0xb70fffe5U: // x = -0x1.1fffcap-17
136 return fputil::round_result_slightly_down(-0x1.20001ap-17f);
137 case 0xbb0ec8c4U: // x = -0x1.1d9188p-9
138 return fputil::round_result_slightly_up(-0x1.1de14ap-9f);
139 }
140
141 // Polymial generated by Sollya with:
142 // > fpminimax(log(1 + x)/x, 7, [|D...|], [-2^-6; 2^-6]);
143 const double COEFFS[7] = {-0x1.0000000000000p-1, 0x1.5555555556aadp-2,
144 -0x1.000000000181ap-2, 0x1.999998998124ep-3,
145 -0x1.55555452e2a2bp-3, 0x1.24adb8cde4aa7p-3,
146 -0x1.0019db915ef6fp-3};
147
148 double xsq = xd * xd;
149 double c0 = fputil::multiply_add(xd, COEFFS[1], COEFFS[0]);
150 double c1 = fputil::multiply_add(xd, COEFFS[3], COEFFS[2]);
151 double c2 = fputil::multiply_add(xd, COEFFS[5], COEFFS[4]);
152 double r = fputil::polyeval(xsq, xd, c0, c1, c2, COEFFS[6]);
153
154 return static_cast<float>(r);
155 }
156
157 } // namespace LIBC_NAMESPACE_DECL
158