number-theory 0.0.22

Fast primality, factorization and elementary number theory for integer types
Documentation 
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

use std::str;
use std::str::FromStr;

use crate::arithmetic::sign::Sign;
use crate::arithmetic::sliceops::*;

// converts u64 to string of length 19
fn string_format(x: u64) -> String {
    let k = x.to_string();
    let leading = (0..(19 - k.len())).map(|_| "0").collect::<String>();
    leading + &k
}

// Naive conversion from Radix-2^64 to Radix-10^19 string, very slow
pub(crate) fn to_string(sign: Sign, digits: Vec<u64>) -> String {
    if digits.is_empty() {
        return "".to_string();
    }

    if digits.len() == 1 {
        let p = digits[0].to_string();
        if sign == Sign::Negative {
            return "-".to_owned() + &p;
        } else {
            return p;
        }
    }

    let mut k = vec![];
    let mut x = digits;
    x.push(0u64);
    loop {
        let idx = sig_pos(&x[..]);

        if idx == 0 {
            break;
        }

        k.push(div_slice(&mut x[..idx], 0x8AC7230489E80000u64));
    }
    k.push(x[0] % 0x8AC7230489E80000u64);

    let mut count = 0usize;
    for i in k.iter().rev() {
        if *i > 0u64 {
            break;
        }
        count += 1;
    }

    k.truncate(k.len() - count);

    let len = k.len() - 1;
    let interim = k[..len]
        .iter()
        .rev()
        .map(|x| string_format(*x))
        .collect::<Vec<String>>();
    let last = k[len].to_string() + &interim.join("");

    if sign == Sign::Negative {
        return "-".to_string() + &last;
    }
    last
}

pub(crate) fn to_hex_string(sign: Sign, digits: Vec<u64>) -> String{
               if digits.is_empty() {
                  return "".to_string();
               }
               let mut k = "0x".to_string();
               
               if sign == Sign::Negative{
                 k = "-".to_string() + &k;
               }
               
               if digits.len()==1{
                 let p = format!("{:0X}",digits[0]);//digits[0].to_string();
                 if sign == Sign::Negative {
                   return "-".to_owned() + &p;
                 } else {
                  return p;
                 }
               }
               for i in digits.iter().rev(){
                 k = k.to_owned() + &format!("{:0X}",i);// &word_char(*i);
               }
              return k
}

pub(crate) fn from_string(string: &str) -> Option<Vec<u64>> {
    let b = string.bytes().all(|c| c.is_ascii_digit());

    if !b {
        return None;
    }

    let ln = 19usize;
    let strln = string.len();
    let strem = strln % ln;
    let t = string.as_bytes();
    let start = 0usize;

    let mut k = vec![];

    for i in 0..strln / ln {
        k.push(str::from_utf8(&t[(strln - (i + 1) * ln)..(strln - i * ln)]).unwrap())
    }
    if strem != 0 {
        // if there is a remaining slice greater than zero
        if str::from_utf8(&t[start..strem]).unwrap() != "" {
            // if the first value is not empty then it pushes it to the vector
            k.push(str::from_utf8(&t[start..strem]).unwrap());
        }
    }
    let x = k
        .iter()
        .rev()
        .map(|x| u64::from_str(x).unwrap())
        .collect::<Vec<u64>>(); // string converted to decimal vector

    let mut z = vec![0];
    for i in 0..x.len() {
        let mut carry = scale_slice(&mut z[..], 0x8AC7230489E80000);
        if carry > 0 {
            z.push(carry)
        }
        carry = add_slice(&mut z[..], &x[i..(i + 1)]) as u64;
        if carry > 0 {
            z.push(carry)
        }
    }
    Some(z)
}