1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
use super::P16E1;
impl P16E1 {
pub const fn tan_pi(self) -> Self {
let ui_a = self.to_bits();
let mut f = ui_a as u64;
let mut sign = f & 0x8000;
if sign != 0 {
f = 0x_0001_0000 - f; }
if f > 31743 {
return if f == 0x8000 { Self::NAR } else { Self::ZERO }; }
if f != 0 {
let mut s: i32;
if (f & 0x4000) != 0 {
s = 16;
while (f & 0x2000) != 0 {
f <<= 1;
s += 2;
}
} else {
s = 14;
while (f & 0x2000) == 0 {
f <<= 1;
s -= 2;
}
}
if (f & 0x1000) != 0 {
s += 1; }
f = (f & 0x0FFF) | 0x1000; f = if s < 0 { f >> -s } else { f << s };
}
f &= 0x_0FFF_FFFF; if f == 0 {
return Self::ZERO;
}
let s = f >> 27; f &= 0x_07FF_FFFF; if f == 0 {
return Self::NAR;
}
if s != 0 {
sign ^= 0x8000; }
if (f & 0x_03FF_FFFF) == 0 {
return Self::from_bits(sign as u16 | 0x4000);
}
if sign != 0 {
f = 0x_0800_0000 - f; }
if (ui_a & 0x8000) != 0 {
f = 0x_0800_0000 - f; }
f = poly(f); let mut s: i32;
if f > 0x_0FFF_FFFF {
s = 12;
while (f & 0x_0100_0000_0000) == 0 {
f <<= 1;
s -= 1;
}
if (s & 1) == 0 {
f &= 0x_00FF_FFFF_FFFF;
}
s = (s >> 1) + 28;
f |= (2_u64 << (14 + s)) - (1_u64 << 42);
} else {
s = 1;
while (f & 0x_0800_0000) == 0 {
f <<= 1;
s += 1;
}
let bit = s & 1;
s = (s >> 1) + 14 + bit;
if bit == 0 {
f &= 0x_07FF_FFFF;
}
f |= 0x_1000_0000;
}
let bit = 1_u64 << (s - 1);
if (f & bit) != 0 {
if ((f & (bit - 1)) != 0) || ((f & (bit << 1)) != 0) {
f += bit;
}
}
f >>= s;
Self::from_bits((if sign != 0 { 0x_0001_0000 - f } else { f }) as u16)
}
}
#[inline]
const fn poly(f: u64) -> u64 {
if f < 0xE001 {
return (f * 102_943) >> 15; }
let fs = f >> 9;
let fsq = (fs * fs) >> 10;
let mut num = (fsq * 182_527) >> 27;
let den = (fsq * 13_335_493) >> 25;
num = (fsq * (3_648_552 - num)) >> 23;
let den = 0x_0800_0000 - ((fsq * (295_106_440 - den)) >> 27);
num = (fs * (105_414_368 - num)) << 11;
num / den
}
#[test]
fn test_tan_pi() {
use rand::Rng;
let mut rng = rand::thread_rng();
for _ in 0..crate::NTESTS16 {
let p_a: P16E1 = rng.gen();
let f_a = f64::from(p_a);
let p = p_a.tan_pi();
let f = (f_a * core::f64::consts::PI).tan();
let expected = P16E1::from(f);
if p.is_zero() || p.is_nar() {
continue;
}
assert_eq!(p, expected);
}
}