1//===-- Single-precision tan 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/tanf.h"
10#include "sincosf_utils.h"
11#include "src/__support/FPUtil/FEnvImpl.h"
12#include "src/__support/FPUtil/FPBits.h"
13#include "src/__support/FPUtil/PolyEval.h"
14#include "src/__support/FPUtil/except_value_utils.h"
15#include "src/__support/FPUtil/multiply_add.h"
16#include "src/__support/FPUtil/nearest_integer.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" // LIBC_TARGET_CPU_HAS_FMA
21
22namespace LIBC_NAMESPACE_DECL {
23
24#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
25// Exceptional cases for tanf.
26constexpr size_t N_EXCEPTS = 6;
27
28constexpr fputil::ExceptValues<float, N_EXCEPTS> TANF_EXCEPTS{{
29 // (inputs, RZ output, RU offset, RD offset, RN offset)
30 // x = 0x1.ada6aap27, tan(x) = 0x1.e80304p-3 (RZ)
31 {0x4d56d355, 0x3e740182, 1, 0, 0},
32 // x = 0x1.862064p33, tan(x) = -0x1.8dee56p-3 (RZ)
33 {0x50431032, 0xbe46f72b, 0, 1, 1},
34 // x = 0x1.af61dap48, tan(x) = 0x1.60d1c6p-2 (RZ)
35 {0x57d7b0ed, 0x3eb068e3, 1, 0, 1},
36 // x = 0x1.0088bcp52, tan(x) = 0x1.ca1edp0 (RZ)
37 {0x5980445e, 0x3fe50f68, 1, 0, 0},
38 // x = 0x1.f90dfcp72, tan(x) = 0x1.597f9cp-1 (RZ)
39 {0x63fc86fe, 0x3f2cbfce, 1, 0, 0},
40 // x = 0x1.a6ce12p86, tan(x) = -0x1.c5612ep-1 (RZ)
41 {0x6ad36709, 0xbf62b097, 0, 1, 0},
42}};
43#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
44
45LLVM_LIBC_FUNCTION(float, tanf, (float x)) {
46 using FPBits = typename fputil::FPBits<float>;
47 FPBits xbits(x);
48 uint32_t x_abs = xbits.uintval() & 0x7fff'ffffU;
49
50 // |x| < pi/32
51 if (LIBC_UNLIKELY(x_abs <= 0x3dc9'0fdbU)) {
52 double xd = static_cast<double>(x);
53
54 // |x| < 0x1.0p-12f
55 if (LIBC_UNLIKELY(x_abs < 0x3980'0000U)) {
56 if (LIBC_UNLIKELY(x_abs == 0U)) {
57 // For signed zeros.
58 return x;
59 }
60 // When |x| < 2^-12, the relative error of the approximation tan(x) ~ x
61 // is:
62 // |tan(x) - x| / |tan(x)| < |x^3| / (3|x|)
63 // = x^2 / 3
64 // < 2^-25
65 // < epsilon(1)/2.
66 // So the correctly rounded values of tan(x) are:
67 // = x + sign(x)*eps(x) if rounding mode = FE_UPWARD and x is positive,
68 // or (rounding mode = FE_DOWNWARD and x is
69 // negative),
70 // = x otherwise.
71 // To simplify the rounding decision and make it more efficient, we use
72 // fma(x, 2^-25, x) instead.
73 // Note: to use the formula x + 2^-25*x to decide the correct rounding, we
74 // do need fma(x, 2^-25, x) to prevent underflow caused by 2^-25*x when
75 // |x| < 2^-125. For targets without FMA instructions, we simply use
76 // double for intermediate results as it is more efficient than using an
77 // emulated version of FMA.
78#if defined(LIBC_TARGET_CPU_HAS_FMA_FLOAT)
79 return fputil::multiply_add(x, 0x1.0p-25f, x);
80#else
81 return static_cast<float>(fputil::multiply_add(xd, 0x1.0p-25, xd));
82#endif // LIBC_TARGET_CPU_HAS_FMA_FLOAT
83 }
84
85 // |x| < pi/32
86 double xsq = xd * xd;
87
88 // Degree-9 minimax odd polynomial of tan(x) generated by Sollya with:
89 // > P = fpminimax(tan(x)/x, [|0, 2, 4, 6, 8|], [|1, D...|], [0, pi/32]);
90 double result =
91 fputil::polyeval(xsq, 1.0, 0x1.555555553d022p-2, 0x1.111111ce442c1p-3,
92 0x1.ba180a6bbdecdp-5, 0x1.69c0a88a0b71fp-6);
93 return static_cast<float>(xd * result);
94 }
95
96#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
97 bool x_sign = xbits.uintval() >> 31;
98 // Check for exceptional values
99 if (LIBC_UNLIKELY(x_abs == 0x3f8a1f62U)) {
100 // |x| = 0x1.143ec4p0
101 float sign = x_sign ? -1.0f : 1.0f;
102
103 // volatile is used to prevent compiler (gcc) from optimizing the
104 // computation, making the results incorrect in different rounding modes.
105 volatile float tmp = 0x1.ddf9f4p0f;
106 tmp = fputil::multiply_add(sign, tmp, sign * 0x1.1p-24f);
107
108 return tmp;
109 }
110#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
111
112 // |x| > 0x1.ada6a8p+27f
113 if (LIBC_UNLIKELY(x_abs > 0x4d56'd354U)) {
114 // Inf or NaN
115 if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) {
116 if (xbits.is_signaling_nan()) {
117 fputil::raise_except_if_required(FE_INVALID);
118 return FPBits::quiet_nan().get_val();
119 }
120
121 if (x_abs == 0x7f80'0000U) {
122 fputil::set_errno_if_required(EDOM);
123 fputil::raise_except_if_required(FE_INVALID);
124 }
125 return x + FPBits::quiet_nan().get_val();
126 }
127#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
128 // Other large exceptional values
129 if (auto r = TANF_EXCEPTS.lookup_odd(x_abs, x_sign);
130 LIBC_UNLIKELY(r.has_value()))
131 return r.value();
132#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
133 }
134
135 // For |x| >= pi/32, we use the definition of tan(x) function:
136 // tan(x) = sin(x) / cos(x)
137 // The we follow the same computations of sin(x) and cos(x) as sinf, cosf,
138 // and sincosf.
139
140 double xd = static_cast<double>(x);
141 double sin_k, cos_k, sin_y, cosm1_y;
142
143 sincosf_eval(xd, x_abs, sin_k, cos_k, sin_y, cosm1_y);
144 // tan(x) = sin(x) / cos(x)
145 // = (sin_y * cos_k + cos_y * sin_k) / (cos_y * cos_k - sin_y * sin_k)
146 using fputil::multiply_add;
147 return static_cast<float>(
148 multiply_add(sin_y, cos_k, multiply_add(cosm1_y, sin_k, sin_k)) /
149 multiply_add(sin_y, -sin_k, multiply_add(cosm1_y, cos_k, cos_k)));
150}
151
152} // namespace LIBC_NAMESPACE_DECL
153

source code of libc/src/math/generic/tanf.cpp