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

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