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
137
138
139
140
141
142
143
144
145
146

//! Arcsine.

use crate::common::consts::ONE;
use crate::common::util::count_leading_ones;
use crate::common::util::round_p;
use crate::defs::Error;
use crate::defs::RoundingMode;
use crate::num::BigFloatNumber;
use crate::ops::consts::Consts;

impl BigFloatNumber {
    /// Computes the arcsine of a number with precision `p`. The result is rounded using the rounding mode `rm`.
    /// This function requires constants cache `cc` for computing the result.
    /// Precision is rounded upwards to the word size.
    ///
    /// ## Errors
    ///
    ///  - InvalidArgument: argument is greater than 1 or smaller than -1, or the precision is incorrect.
    ///  - MemoryAllocation: failed to allocate memory.
    pub fn asin(&self, p: usize, rm: RoundingMode, cc: &mut Consts) -> Result<Self, Error> {
        let p = round_p(p);

        if self.abs_cmp(&ONE) == 0 {
            let mut pi = cc.pi(p, rm)?;

            pi.set_exponent(pi.get_exponent() - 1);
            pi.set_sign(self.get_sign());

            return Ok(pi);
        }

        let mut additional_prec = 2;
        if self.get_exponent() == 0 {
            additional_prec += count_leading_ones(self.get_mantissa_digits());
        }

        let mut x = self.clone()?;

        let p_x = p + additional_prec;
        x.set_precision(p_x, RoundingMode::None)?;

        // arcsin(x) = arctan(x / sqrt(1 - x^2))
        let xx = x.mul(&x, p_x, RoundingMode::None)?;
        let t = ONE.sub(&xx, p_x, RoundingMode::None)?;
        let s = t.sqrt(p_x, RoundingMode::None)?;
        let d = x.div(&s, p_x, RoundingMode::None)?;

        let mut ret = d.atan(p_x, RoundingMode::None, cc)?;

        ret.set_precision(p, rm)?;

        Ok(ret)
    }
}

#[cfg(test)]
mod tests {

    use crate::common::util::random_subnormal;

    use super::*;

    #[test]
    fn test_arcsine() {
        let mut cc = Consts::new().unwrap();

        let rm = RoundingMode::ToEven;
        let p = 64;
        let mut n1 = BigFloatNumber::from_word(4294967295, p).unwrap();
        n1.set_exponent(0);
        //println!("{}", n1.format(crate::Radix::Dec, RoundingMode::None).unwrap());
        let _n2 = n1.asin(p, rm, &mut cc).unwrap();
        //println!("{:?}", n2.format(crate::Radix::Dec, rm).unwrap());

        // asymptotic & extrema testing
        let p = 320;
        let n1 = BigFloatNumber::parse(
            "F.FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF2DC85F7E77EC487_e-1",
            crate::Radix::Hex,
            p,
            RoundingMode::None,
        )
        .unwrap();
        let n2 = n1.asin(p, rm, &mut cc).unwrap();
        let n3 = BigFloatNumber::parse("1.921FB54442D18469898CC51701B839A200000000000000004D3C337F7C8D419EBBFC39B4BEC14AF6_e+0", crate::Radix::Hex, p, RoundingMode::None).unwrap();

        assert!(n2.cmp(&n3) == 0);

        // near zero
        let n1 = BigFloatNumber::parse("1.921FB54442D18469898CC51701B839A200000000000000004D3C337F7C8D419EBBFC39B4BEC14AF6_e-10", crate::Radix::Hex, p, RoundingMode::None).unwrap();
        let n2 = n1.asin(p, rm, &mut cc).unwrap();
        let n3 = BigFloatNumber::parse("1.921FB54442D18469898CC51701B839A2A55DE7312DF295F5AB0362F0A77F89C5756A9380CF056D90_e-10", crate::Radix::Hex, p, RoundingMode::None).unwrap();

        //println!("{:?}", n2.format(crate::Radix::Hex, rm).unwrap());

        assert!(n2.cmp(&n3) == 0);

        let d1 = BigFloatNumber::max_value(p).unwrap();
        let d2 = BigFloatNumber::min_value(p).unwrap();
        let d3 = BigFloatNumber::min_positive(p).unwrap();
        let zero = BigFloatNumber::new(1).unwrap();

        let mut half_pi = cc.pi(p, RoundingMode::ToEven).unwrap();
        half_pi.set_exponent(1);

        assert!(d1.asin(p, rm, &mut cc).is_err());
        assert!(d2.asin(p, rm, &mut cc).is_err());
        assert!(d3.asin(p, rm, &mut cc).unwrap().cmp(&d3) == 0);
        assert!(zero.asin(p, rm, &mut cc).unwrap().is_zero());
        assert!(ONE.asin(p, rm, &mut cc).unwrap().cmp(&half_pi) == 0);
        assert!(
            ONE.neg()
                .unwrap()
                .asin(p, rm, &mut cc)
                .unwrap()
                .cmp(&half_pi.neg().unwrap())
                == 0
        );

        // subnormal arg
        let n1 = random_subnormal(p);
        assert!(n1.asin(p, rm, &mut cc).unwrap().cmp(&n1) == 0);
    }

    #[ignore]
    #[test]
    #[cfg(feature = "std")]
    fn arcsine_perf() {
        let mut cc = Consts::new().unwrap();
        let p = 160;

        let mut n = vec![];
        for _ in 0..10000 {
            n.push(BigFloatNumber::random_normal(p, -5, 0).unwrap());
        }

        for _ in 0..5 {
            let start_time = std::time::Instant::now();
            for ni in n.iter() {
                let _f = ni.asin(p, RoundingMode::ToEven, &mut cc).unwrap();
            }
            let time = start_time.elapsed();
            println!("{}", time.as_millis());
        }
    }
}