1//===-- Single-precision tanpi 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#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_TANPIF_H
10#define LLVM_LIBC_SRC___SUPPORT_MATH_TANPIF_H
11
12#include "sincosf_utils.h"
13#include "src/__support/FPUtil/FEnvImpl.h"
14#include "src/__support/FPUtil/FPBits.h"
15#include "src/__support/FPUtil/cast.h"
16#include "src/__support/FPUtil/except_value_utils.h"
17#include "src/__support/FPUtil/multiply_add.h"
18#include "src/__support/common.h"
19#include "src/__support/macros/config.h"
20#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
21
22namespace LIBC_NAMESPACE_DECL {
23
24namespace math {
25
26LIBC_INLINE float tanpif(float x) {
27 using namespace sincosf_utils_internal;
28
29 using FPBits = typename fputil::FPBits<float>;
30 FPBits xbits(x);
31
32#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
33 constexpr size_t N_EXCEPTS = 3;
34 constexpr fputil::ExceptValues<float, N_EXCEPTS> TANPIF_EXCEPTS{.values: {
35 // (input, RZ output, RU offset, RD offset, RN offset)
36 {.input: 0x38F26685, .rnd_towardzero_result: 0x39BE6182, .rnd_upward_offset: 1, .rnd_downward_offset: 0, .rnd_tonearest_offset: 0},
37 {.input: 0x3E933802, .rnd_towardzero_result: 0x3FA267DD, .rnd_upward_offset: 1, .rnd_downward_offset: 0, .rnd_tonearest_offset: 0},
38 {.input: 0x3F3663FF, .rnd_towardzero_result: 0xBFA267DD, .rnd_upward_offset: 0, .rnd_downward_offset: 1, .rnd_tonearest_offset: 0},
39 }};
40#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
41
42 uint32_t x_u = xbits.uintval();
43 uint32_t x_abs = x_u & 0x7fff'ffffU;
44 double xd = static_cast<double>(xbits.get_val());
45
46 // Handle exceptional values
47 if (LIBC_UNLIKELY(x_abs <= 0x3F3663FF)) {
48 if (LIBC_UNLIKELY(x_abs == 0U))
49 return x;
50
51#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
52 bool x_sign = x_u >> 31;
53
54 if (auto r = TANPIF_EXCEPTS.lookup_odd(x_abs, sign: x_sign);
55 LIBC_UNLIKELY(r.has_value()))
56 return r.value();
57#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
58 }
59
60 // Numbers greater or equal to 2^23 are always integers, or infinity, or NaN
61 if (LIBC_UNLIKELY(x_abs >= 0x4B00'0000)) {
62 // x is inf or NaN.
63 if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) {
64 if (xbits.is_signaling_nan()) {
65 fputil::raise_except_if_required(FE_INVALID);
66 return FPBits::quiet_nan().get_val();
67 }
68
69 if (x_abs == 0x7f80'0000U) {
70 fputil::set_errno_if_required(EDOM);
71 fputil::raise_except_if_required(FE_INVALID);
72 }
73
74 return x + FPBits::quiet_nan().get_val();
75 }
76
77 return FPBits::zero(sign: xbits.sign()).get_val();
78 }
79
80 // Range reduction:
81 // For |x| > 1/32, we perform range reduction as follows:
82 // Find k and y such that:
83 // x = (k + y) * 1/32
84 // k is an integer
85 // |y| < 0.5
86 //
87 // This is done by performing:
88 // k = round(x * 32)
89 // y = x * 32 - k
90 //
91 // Once k and y are computed, we then deduce the answer by the formula:
92 // tan(x) = sin(x) / cos(x)
93 // = (sin_y * cos_k + cos_y * sin_k) / (cos_y * cos_k - sin_y * sin_k)
94 double sin_k, cos_k, sin_y, cosm1_y;
95 sincospif_eval(xd, sin_k, cos_k, sin_y, cosm1_y);
96
97 if (LIBC_UNLIKELY(sin_y == 0 && cos_k == 0)) {
98 fputil::set_errno_if_required(EDOM);
99 fputil::raise_except_if_required(FE_DIVBYZERO);
100
101 int32_t x_mp5_i = static_cast<int32_t>(xd - 0.5);
102 return FPBits::inf(sign: (x_mp5_i & 0x1) ? Sign::NEG : Sign::POS).get_val();
103 }
104
105 using fputil::multiply_add;
106 return fputil::cast<float>(
107 x: multiply_add(x: sin_y, y: cos_k, z: multiply_add(x: cosm1_y, y: sin_k, z: sin_k)) /
108 multiply_add(x: sin_y, y: -sin_k, z: multiply_add(x: cosm1_y, y: cos_k, z: cos_k)));
109}
110
111} // namespace math
112
113} // namespace LIBC_NAMESPACE_DECL
114
115#endif // LLVM_LIBC_SRC___SUPPORT_MATH_TANPIF_H
116