1 | /* Compute cosine of argument. |
2 | Copyright (C) 2017-2018 Free Software Foundation, Inc. |
3 | This file is part of the GNU C Library. |
4 | |
5 | The GNU C Library is free software; you can redistribute it and/or |
6 | modify it under the terms of the GNU Lesser General Public |
7 | License as published by the Free Software Foundation; either |
8 | version 2.1 of the License, or (at your option) any later version. |
9 | |
10 | The GNU C Library is distributed in the hope that it will be useful, |
11 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
13 | Lesser General Public License for more details. |
14 | |
15 | You should have received a copy of the GNU Lesser General Public |
16 | License along with the GNU C Library; if not, see |
17 | <http://www.gnu.org/licenses/>. */ |
18 | |
19 | #include <errno.h> |
20 | #include <math.h> |
21 | #include <math_private.h> |
22 | #include <libm-alias-float.h> |
23 | #include "s_sincosf.h" |
24 | |
25 | #ifndef COSF |
26 | # define COSF_FUNC __cosf |
27 | #else |
28 | # define COSF_FUNC COSF |
29 | #endif |
30 | |
31 | float |
32 | COSF_FUNC (float x) |
33 | { |
34 | double theta = x; |
35 | double abstheta = fabs (theta); |
36 | if (isless (abstheta, M_PI_4)) |
37 | { |
38 | double cx; |
39 | if (abstheta >= 0x1p-5) |
40 | { |
41 | const double theta2 = theta * theta; |
42 | /* Chebyshev polynomial of the form for cos: |
43 | * 1 + x^2 (C0 + x^2 (C1 + x^2 (C2 + x^2 (C3 + x^2 * C4)))). */ |
44 | cx = C3 + theta2 * C4; |
45 | cx = C2 + theta2 * cx; |
46 | cx = C1 + theta2 * cx; |
47 | cx = C0 + theta2 * cx; |
48 | cx = 1. + theta2 * cx; |
49 | return cx; |
50 | } |
51 | else if (abstheta >= 0x1p-27) |
52 | { |
53 | /* A simpler Chebyshev approximation is close enough for this range: |
54 | * 1 + x^2 (CC0 + x^3 * CC1). */ |
55 | const double theta2 = theta * theta; |
56 | cx = CC0 + theta * theta2 * CC1; |
57 | cx = 1.0 + theta2 * cx; |
58 | return cx; |
59 | } |
60 | else |
61 | { |
62 | /* For small enough |theta|, this is close enough. */ |
63 | return 1.0 - abstheta; |
64 | } |
65 | } |
66 | else /* |theta| >= Pi/4. */ |
67 | { |
68 | if (isless (abstheta, 9 * M_PI_4)) |
69 | { |
70 | /* There are cases where FE_UPWARD rounding mode can |
71 | produce a result of abstheta * inv_PI_4 == 9, |
72 | where abstheta < 9pi/4, so the domain for |
73 | pio2_table must go to 5 (9 / 2 + 1). */ |
74 | unsigned int n = (abstheta * inv_PI_4) + 1; |
75 | theta = abstheta - pio2_table[n / 2]; |
76 | return reduced_cos (theta, n); |
77 | } |
78 | else if (isless (abstheta, INFINITY)) |
79 | { |
80 | if (abstheta < 0x1p+23) |
81 | { |
82 | unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1; |
83 | double x = n / 2; |
84 | theta = (abstheta - x * PI_2_hi) - x * PI_2_lo; |
85 | /* Argument reduction needed. */ |
86 | return reduced_cos (theta, n); |
87 | } |
88 | else /* |theta| >= 2^23. */ |
89 | { |
90 | x = fabsf (x); |
91 | int exponent; |
92 | GET_FLOAT_WORD (exponent, x); |
93 | exponent = (exponent >> FLOAT_EXPONENT_SHIFT) |
94 | - FLOAT_EXPONENT_BIAS; |
95 | exponent += 3; |
96 | exponent /= 28; |
97 | double a = invpio4_table[exponent] * x; |
98 | double b = invpio4_table[exponent + 1] * x; |
99 | double c = invpio4_table[exponent + 2] * x; |
100 | double d = invpio4_table[exponent + 3] * x; |
101 | uint64_t l = a; |
102 | l &= ~0x7; |
103 | a -= l; |
104 | double e = a + b; |
105 | l = e; |
106 | e = a - l; |
107 | if (l & 1) |
108 | { |
109 | e -= 1.0; |
110 | e += b; |
111 | e += c; |
112 | e += d; |
113 | e *= M_PI_4; |
114 | return reduced_cos (e, l + 1); |
115 | } |
116 | else |
117 | { |
118 | e += b; |
119 | e += c; |
120 | e += d; |
121 | if (e <= 1.0) |
122 | { |
123 | e *= M_PI_4; |
124 | return reduced_cos (e, l + 1); |
125 | } |
126 | else |
127 | { |
128 | l++; |
129 | e -= 2.0; |
130 | e *= M_PI_4; |
131 | return reduced_cos (e, l + 1); |
132 | } |
133 | } |
134 | } |
135 | } |
136 | else |
137 | { |
138 | int32_t ix; |
139 | GET_FLOAT_WORD (ix, abstheta); |
140 | /* cos(Inf or NaN) is NaN. */ |
141 | if (ix == 0x7f800000) /* Inf. */ |
142 | __set_errno (EDOM); |
143 | return x - x; |
144 | } |
145 | } |
146 | } |
147 | |
148 | #ifndef COSF |
149 | libm_alias_float (__cos, cos) |
150 | #endif |
151 | |