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
147
148
149
150
151
152
153
154

//! Hyperbolic arccosine.

use crate::common::consts::ONE;
use crate::common::util::count_leading_zeroes_skip_first;
use crate::common::util::round_p;
use crate::defs::Error;
use crate::defs::RoundingMode;
use crate::num::BigFloatNumber;
use crate::Consts;
use crate::Sign;
use crate::EXPONENT_MAX;

impl BigFloatNumber {
    /// Computes the hyperbolic arccosine 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
    ///
    ///  - ExponentOverflow: the result is too large or too small number.
    ///  - MemoryAllocation: failed to allocate memory.
    ///  - InvalidArgument: when `self` < 1, or the precision is incorrect.
    pub fn acosh(&self, p: usize, rm: RoundingMode, cc: &mut Consts) -> Result<Self, Error> {
        let p = round_p(p);

        let cmpone = self.cmp(&ONE);
        if cmpone == 0 {
            return Self::new(p);
        } else if cmpone < 0 {
            return Err(Error::InvalidArgument);
        }

        if (self.get_exponent() as isize - 1) / 2 > self.get_mantissa_max_bit_len() as isize + 2 {
            // acosh(x) = ln(2*x)
            if self.get_exponent() == EXPONENT_MAX {
                Err(Error::ExponentOverflow(Sign::Pos))
            } else {
                let mut x = self.clone()?;
                x.set_exponent(x.get_exponent() + 1);
                x.ln(p, rm, cc)
            }
        } else {
            // ln(x + sqrt(x*x - 1))

            let mut additional_prec = 0;
            if self.get_exponent() == 1 {
                additional_prec = count_leading_zeroes_skip_first(self.m.get_digits());
            }

            let mut x = self.clone()?;

            let p_x = p + 3 + additional_prec;
            x.set_precision(p_x, RoundingMode::None)?;

            let xx = x.mul(&x, p_x, RoundingMode::None)?;

            let d1 = xx.sub(&ONE, p_x, RoundingMode::None)?;

            let d2 = d1.sqrt(p_x, RoundingMode::None)?;

            let d3 = d2.add(&x, p_x, RoundingMode::None)?;

            d3.ln(p, rm, cc)
        }
    }
}

#[cfg(test)]
mod tests {

    use crate::Exponent;

    use super::*;

    #[test]
    fn test_acosh() {
        let p = 320;
        let mut cc = Consts::new().unwrap();
        let rm = RoundingMode::ToEven;
        let n1 = BigFloatNumber::from_word(2, p).unwrap();
        let _n2 = n1.acosh(p, rm, &mut cc).unwrap();
        //println!("{:?}", n2.format(crate::Radix::Bin, rm).unwrap());

        // near 1
        let p = 448;
        let n1 = BigFloatNumber::parse("1.0000000000000000000000000000000000000000000B56A0EBA6F7D47E21A7B2A7806A698BABAF2F05BC61E2F8FB50FE0B98F55B181AC9C8_e+0", crate::Radix::Hex, p, RoundingMode::None).unwrap();
        let n2 = n1.acosh(p, rm, &mut cc).unwrap();
        let n3 = BigFloatNumber::parse("4.C31368910963B1A1BCFC0EDBD393FB7A5E876F9751D93A20E7E48EC0D16090ADA5F46DF2184D32A19C500088EA09CBD4F23DF713113D8A58_e-16", crate::Radix::Hex, p, RoundingMode::None).unwrap();

        // println!("{:?}", n1.format(crate::Radix::Bin, rm).unwrap());
        // println!("{:?}", n2.format(crate::Radix::Hex, rm).unwrap());

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

        // large exp
        let p = 320;
        let n1 = BigFloatNumber::parse("1.921FB54442D18469898CC51701B839A200000000000000004D3C337F7C8D419EBBFC39B4BEC14AF6_e+1000", crate::Radix::Hex, p, RoundingMode::None).unwrap();
        let n2 = n1.acosh(p, rm, &mut cc).unwrap();
        let n3 = BigFloatNumber::parse("2.C5DAB0AF9025886C3364C7B6D6741EB19D4FB009D3F92CA21B77498D9F0666363C665F2F324EAEC8_e+3", crate::Radix::Hex, p, RoundingMode::None).unwrap();

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

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

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

        assert!(d1.acosh(p, rm, &mut cc).unwrap_err() == Error::ExponentOverflow(Sign::Pos));

        d1.set_exponent(d1.get_exponent() - 1);
        let d4 = d1.acosh(p, rm, &mut cc).unwrap();
        let d5 = d4.cosh(p, rm, &mut cc).unwrap();
        let mut eps = ONE.clone().unwrap();
        eps.set_exponent(
            d1.get_exponent() - p as Exponent + core::mem::size_of::<Exponent>() as Exponent * 8,
        );

        assert!(
            d1.sub(&d5, p, RoundingMode::ToEven)
                .unwrap()
                .abs()
                .unwrap()
                .cmp(&eps)
                < 0
        );

        assert!(d2.acosh(p, rm, &mut cc).unwrap_err() == Error::InvalidArgument);
        assert!(d3.acosh(p, rm, &mut cc).unwrap_err() == Error::InvalidArgument);

        assert!(ONE.acosh(p, rm, &mut cc).unwrap().is_zero());
    }

    #[ignore]
    #[test]
    #[cfg(feature = "std")]
    fn acosh_perf() {
        let mut cc = Consts::new().unwrap();
        let mut n = vec![];
        let p = 160;
        for _ in 0..10000 {
            n.push(BigFloatNumber::random_normal(p, 0, 5).unwrap());
        }

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