numera 0.5.0

numbers
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
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165

// numera::number::integer::q::rational
//
//!
//

use crate::number::{
    integer::*,
    rational::*,
    traits::{ConstOne, ConstZero, Ident},
};

/// Implements the `Rational` trait on sized rationals.
macro_rules! impl_rational {
    // Args:
    // $(
    //   `$t`: the type of the rational. E.g. Rational16.
    //   `$num`: the type of the numerator. E.g. Integer16.
    //   `$den`: the type of the denominator. E.g. NonZeroInteger16.
    // ),+
    (many: $(($t:ident, $num:ident, $den:ident)),+) => {
        $( impl_rational![single: $t, $num, $den]; )+
    };

    // Args:
    //   `$t`: the type of the rational. E.g. Rational16.
    //   `$num`: the type of the numerator. E.g. Integer16.
    //   `$den`: the type of the denominator. E.g. NonZeroInteger16.
    (single: $t:ident, $num:ident, $den:ident) => {
        impl Rational for $t {
            #[inline]
            fn is_integer(&self) -> bool {
                self.num % self.den.into() == $num::ZERO
            }
            #[inline]
            fn is_proper(&self) -> bool {
                // IMPROVE when impl abs for Signed
                self.num.0.abs() < self.den.0.get().abs()
            }
            #[inline]
            fn is_reduced(&self) -> bool {
                // IMPROVE when impl From for references.
                // self.num.gcd(self.den.into()).unwrap() == $num::ONE
                self.num.integer_gcd(&Into::<$num>::into(self.den)).unwrap() == $num::ONE
            }
            #[inline]
            fn reduce(&mut self) {
                let gcd_value = self.num.integer_gcd(&Into::<$num>::into(self.den)).unwrap();

                self.num /= gcd_value;

                // RETHINK safe/unsafe
                // #[cfg(feature = "safe")]
                {
                    self.den = $den::new(self.den.0.get() / gcd_value.0).unwrap();
                    // BENCH:ALTERNATIVE:
                    // self.den = $den::from_parts((Into::<$num>::into(self.den) / gcd_value).0).unwrap();
                }

                // RETHINK safe/unsafe
                // #[cfg(not(feature = "safe"))]
                // // SAFETY: the value returned by gcd can't be zero.
                // { unsafe { self.den = $den::from_parts_unchecked(self.den.0.get() / gcd_value.0); } }
            }

            #[inline]
            fn reduced(&self) -> Self {
                let gcd_value = self.num.integer_gcd(&Into::<$num>::into(self.den)).unwrap();

                $t {
                    num: self.num / gcd_value,

                    // RETHINK safe/unsafe
                    // #[cfg(feature = "safe")]
                    den: $den::new(self.den.0.get() / gcd_value.0).unwrap(),

                    // RETHINK safe/unsafe
                    // #[cfg(not(feature = "safe"))]
                    // // SAFETY: the value returned by gcd can't be zero.
                    // den: unsafe { $den::from_parts_unchecked(self.den.0.get() / gcd_value.0) },
                }
            }

            #[inline]
            fn invert(&mut self) {
                if !self.num.is_zero() {
                    let old_num = self.num;
                    self.num = self.den.into();

                    // RETHINK safe/unsafe
                    // #[cfg(feature = "safe")]
                    { self.den = $den::new(old_num.0).unwrap(); }

                    // RETHINK safe/unsafe
                    // #[cfg(not(feature = "safe"))]
                    // // SAFETY: we've just checked the value is not 0.
                    // { self.den = unsafe { $den::from_parts_unchecked(old_num.0) }; }
                }
            }
            #[inline]
            fn inverted(&self) -> Self {
                if self.num.is_zero() {
                    *self
                } else {
                    $t {
                        num: self.den.into(),

                        // RETHINK safe/unsafe
                        // #[cfg(feature = "safe")]
                        // den: $den::from_parts(self.num.0).unwrap(),
                        den: $den::new(self.num.0).unwrap(),

                        // RETHINK safe/unsafe
                        // #[cfg(not(feature = "safe"))]
                        // // SAFETY: we've just checked the value is not 0.
                        // den: unsafe { $den::from_parts_unchecked(self.num.0) },
                    }
                }
            }
        }
    };
}

impl_rational![
    many: (Rational8, Z8, N0z8),
    (Rational16, Z16, N0z16),
    (Rational32, Z32, N0z32),
    (Rational64, Z64, N0z64),
    (Rational128, Z128, N0z128)
];

#[cfg(test)]
mod tests {
    use crate::all::*;

    #[test]
    fn q_rational() -> NumeraResult<()> {
        // Integer
        //
        // true
        assert![Q8::new(0, 7)?.is_integer()];
        assert![Q8::new(1, 1)?.is_integer()];
        assert![Q8::new(14, 1)?.is_integer()];
        assert![Q8::new(32, 8)?.is_integer()];
        // false
        assert![!Q8::new(1, 2)?.is_integer()];
        assert![!Q8::new(32, 9)?.is_integer()];

        // Reduce
        //
        // true
        assert![Q8::new(3, 14)?.is_reduced()];
        // false
        assert![!Q8::new(21, 98)?.is_reduced()];
        //
        assert_eq![Q8::new(21, 98)?.reduced(), Q8::new(3, 14)?];
        assert_eq![Q8::new(0, 98)?.reduced(), Q8::new(0, 1)?];

        // Invert
        //
        assert_eq![Q8::new(21, 98)?.inverted(), Q8::new(98, 21)?];
        assert_eq![Q8::new(0, 5)?.inverted(), Q8::new(0, 5)?];

        Ok(())
    }
}