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
166

#[cfg(test)]
extern crate md5;
extern crate rug;

pub mod internal;

use std::cmp::Ordering;
use rug::{Integer, Rational};
use rug::ops::Pow;
use internal::*;

/// Represents a mathematical expression of the form `s √(n / d)` where
///
/// - `s` is a sign (`-1`, `0`, or `+1`),
/// - `n` is a nonnegative numerator, and
/// - `d` is a positive denominator.
///
/// This can be converted to a floating-point number via `f64::from(…)`.
///
/// Defaults to zero.
#[derive(Clone, Debug, Default, PartialEq, Eq, Hash, PartialOrd, Ord)]
pub struct SignedSqrtRational(Rational);

impl SignedSqrtRational {
    /// Construct a `SignedSqrtRational` equal to `c √r`.
    #[inline]
    pub fn new(c: Integer, r: Rational) -> Self {
        let sign = Rational::from(ordering_to_i32(c.sign()));
        let radical = Rational::from(c.pow(2)) * r;
        SignedSqrtRational(sign * radical)
    }

    /// Equivalent to `self.cmp(&Self::zero())`.
    #[inline]
    pub fn sign(&self) -> Ordering {
        self.0.sign()
    }

    /// Returns the squared value of the expression.
    #[inline]
    pub fn sq(self) -> Rational {
        self.signed_sq().abs()
    }

    /// Returns the squared value of the expression, with the sign adjusted to
    /// match the sign of the original expression.
    #[inline]
    pub fn signed_sq(self) -> Rational {
        self.0
    }
}

impl From<SignedSqrtRational> for f32 {
    #[inline]
    fn from(s: SignedSqrtRational) -> Self {
        let sign = ordering_to_i32(s.sign()) as f32;
        let radical = s.sq().to_f32().sqrt();
        sign * radical
    }
}

impl From<SignedSqrtRational> for f64 {
    #[inline]
    fn from(s: SignedSqrtRational) -> Self {
        let sign = ordering_to_i32(s.sign()) as f64;
        let radical = s.sq().to_f64().sqrt();
        sign * radical
    }
}

/// Calculate Clebsch-Gordan coefficients.
///
/// ```text
/// ⟨j1 j2 m1 m2|j1 j2 j12 m12⟩
/// ```
pub fn clebsch_gordan(
    tj1: i32,
    tm1: i32,
    tj2: i32,
    tm2: i32,
    tj12: i32,
    tm12: i32,
) -> SignedSqrtRational
{
    let SignedSqrtRational(z) = wigner_3jm_raw_c(tj1, tm1, tj2, tm2, tj12, -tm12);
    SignedSqrtRational(z * Rational::from(tj12 + 1))
}

/// Calculates Wigner 3-jm symbols.
///
/// ```text
/// ⎛j1 j2 j3⎞
/// ⎝m1 m2 m3⎠
/// ```
pub fn wigner_3jm(
    tj1: i32,
    tm1: i32,
    tj2: i32,
    tm2: i32,
    tj3: i32,
    tm3: i32,
) -> SignedSqrtRational
{
    let sign = Rational::from(phase((tj1 - tj2 - tm3) / 2));
    let SignedSqrtRational(radical) =
        wigner_3jm_raw_c (tj1, tm1, tj2, tm2, tj3, tm3);
    SignedSqrtRational(sign * radical)
}

/// Calculates Wigner 6-j symbols.
///
/// ```text
/// ⎧j1 j2 j3⎫
/// ⎩j4 j5 j6⎭
/// ```
pub fn wigner_6j(
    tj1: i32,
    tj2: i32,
    tj3: i32,
    tj4: i32,
    tj5: i32,
    tj6: i32,
) -> SignedSqrtRational
{
    if triangle_condition(tj1, tj2, tj3) &&
        triangle_condition(tj1, tj5, tj6) &&
        triangle_condition(tj4, tj2, tj6) &&
        triangle_condition(tj4, tj5, tj3)
    {
        wigner_6j_raw(tj1, tj2, tj3, tj4, tj5, tj6)
    } else {
        Default::default()
    }
}

/// Calculates Wigner 9-j symbols.
///
/// ```text
/// ⎧ja jb jc⎫
/// ⎨jd je jf⎬
/// ⎩jg jh ji⎭
/// ```
pub fn wigner_9j(
    tja: i32,
    tjb: i32,
    tjc: i32,
    tjd: i32,
    tje: i32,
    tjf: i32,
    tjg: i32,
    tjh: i32,
    tji: i32,
) -> SignedSqrtRational
{
    if triangle_condition(tja, tjb, tjc) &&
        triangle_condition(tjd, tje, tjf) &&
        triangle_condition(tjg, tjh, tji) &&
        triangle_condition(tja, tjd, tjg) &&
        triangle_condition(tjb, tje, tjh) &&
        triangle_condition(tjc, tjf, tji)
    {
        wigner_9j_raw(tja, tjb, tjc, tjd, tje, tjf, tjg, tjh, tji)
    } else {
        Default::default()
    }
}