rmath 0.1.5

A rust math library
Documentation 
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/// random number generated by the Mersenne Twister Algorithm

use crate::rand::{Seed, Result, PrimitiveType, RandError, RandErrKind, Source};
use std::ops::Shl;
use std::fmt::Debug;


/// Mersenne Twister Algorithm
#[derive(Clone)]
pub struct MersenneTwisterRand<T> {
    word_size: T,
    state_size: T,
    shift_size: T,
    mask_bits: T,
    xor_mask: T,
    tempering_u: T,
    tempering_d: T,
    tempering_s: T,
    tempering_b: T,
    tempering_t: T,
    tempering_c: T,
    shift_l: T,
    init_multiplier: T,
    
    idx: T,
    seed: std::result::Result<T, T>,
    state: Vec<T>,
}

impl<T> MersenneTwisterRand<T> 
    where T: PrimitiveType + PartialOrd<T> + Shl<Output = T> + Default + Debug + Copy {
    /// `w`: word size in number bits to determine the range of values generated by the Rand, 0 < w <= (sizeof(T)*8);
    /// `n`: degree of recurrence;
    /// `m`, middle word, an offset used in the recurrence relation defining the series x, 1 <= m <= n 
    /// `r`, separation point of one word, or the number of bits of the lower bitmask, 0 < r < w
    /// `a`, coefficients of the rational normal form twist matrix 0< a <= ((1<<w) - 1)
    /// `u`, additional Mersenne Twister tempering bit shifts, 0< u < w
    /// `d`, additional Mersenne Twister tempering bit masks, 0<d<=((1<<w)-1)
    /// `s`, TGFSR(R) tempering bit shifts, 0< s<w
    /// `b`, TGFSR(R) tempering bitmasks, 0<b<=((1<<w)-1)
    /// `t`, TGFSR(R) tempering bit shifts, 0< t<w
    /// `c`, TGFSR(R) tempering bitmasks, 0<c<=((1<<w)-1)
    /// `l`, additional Mersenne Twister tempering bit shifts, 0<=l<w
    /// `f`, initialization multiplier, 0<f<=((1<<w)-1)
    pub fn new<Sd: Seed<T>>(sd: &Sd, w: T, n: T, m: T, r: T, a: T,
                            u_d: (T, T), s_b: (T, T), t_c: (T, T), l: T, f: T) -> Result<Self> {
        if w == T::default() || m == T::default() || r == T::default() || a == T::default() || 
            u_d == (T::default(), T::default()) || s_b == (T::default(), T::default()) ||
            t_c == (T::default(), T::default()) || l == T::default() || f == T::default() {
            Err(RandError::new(RandErrKind::InvalidRngPara, format!("all parameters cannot be the {:?}", T::default())))
        } else if  m > n {
            Err(RandError::new(RandErrKind::InvalidRngPara, "m must be satisfy the relation: m <= n"))
        } else if w > T::bits_len() {
            Err(RandError::new(RandErrKind::InvalidRngPara, format!("w must be satisfy the relation: m <= {:?}", T::bits_len())))
        } else if r >= w {
            Err(RandError::new(RandErrKind::InvalidRngPara, "r must be less than w"))
        } else if u_d.0 >= w {
            Err(RandError::new(RandErrKind::InvalidRngPara, "u must be less than w"))
        } else if s_b.0 >= w {
            Err(RandError::new(RandErrKind::InvalidRngPara, "s must be less than w"))
        } else if t_c.0 >= w {
            Err(RandError::new(RandErrKind::InvalidRngPara, "t must be less than w"))
        } else if l >= w {
            Err(RandError::new(RandErrKind::InvalidRngPara, "l must be less than w"))
        } else if a > w.mask() {
            Err(RandError::new(RandErrKind::InvalidRngPara, "a must be less than or equal to ((1<<w) - 1)"))
        } else if u_d.1 > w.mask() {
            Err(RandError::new(RandErrKind::InvalidRngPara, "d must be less than  or equal to ((1<<w) - 1)"))
        } else if s_b.1 > w.mask() {
            Err(RandError::new(RandErrKind::InvalidRngPara, "b must be less than  or equal to ((1<<w) - 1)"))
        } else if t_c.1 > w.mask() {
            Err(RandError::new(RandErrKind::InvalidRngPara, "c must be less than  or equal to ((1<<w) - 1)"))
        } else if f > w.mask() {
            Err(RandError::new(RandErrKind::InvalidRngPara, "f must be less than  or equal to ((1<<w) - 1)"))
        } else {
            sd.seed().map(|x| {
                Self {
                    word_size: w,
                    state_size: n,
                    shift_size: m,
                    mask_bits: r,
                    xor_mask: a,
                    tempering_u: u_d.0,
                    tempering_d: u_d.1,
                    tempering_s: s_b.0,
                    tempering_b: s_b.1,
                    tempering_t: t_c.0,
                    tempering_c: t_c.1,
                    shift_l: l,
                    init_multiplier: f,
                    seed: Err(x),
                    idx: n,
                    state: Vec::new(),
                }
            })
        }
    }
}

macro_rules! mtr_impl {
    ($Type0: ty) => {
        impl MersenneTwisterRand<$Type0> {
            fn check_init(&mut self) {
                match self.seed {
                    Err(seed) => {
                        self.state.clear();
                        let n = self.state_size as usize;
                        self.state.reserve(n.saturating_sub(self.state.capacity()));
                        let mut last = seed & self.word_size.mask();
                        self.state.push(last);
                        let n = n as $Type0;
                        (1..n).for_each(|i| {
                            last ^= last >> (self.word_size - 2);
                            last = last.overflowing_mul(self.init_multiplier).0;
                            last = last.overflowing_add(i).0;
                            last &= self.word_size.mask();
                            self.state.push(last);
                        });
                        self.idx = self.state_size;
                        self.seed = Ok(seed);
                    },
                    _ => {},
                }
            }
            
            fn gen_rand(&mut self) {
                let upper_mask: $Type0 = (!(<$Type0>::default())) << self.mask_bits;
                let lower_mask: $Type0 = !upper_mask;
                let k = (self.state_size - self.shift_size) as usize;
                (0..k).for_each(|i| {
                    let y = (self.state[i] & upper_mask) | (self.state[i+1] & lower_mask);
                    self.state[i] = (self.state[i+(self.shift_size as usize)] ^ (y >> 1)) ^
                        (if (y & 0x1) > 0 {self.xor_mask} else {0});
                });
                let n = (self.state_size - 1) as usize;
                let mut j = 0;
                (k..n).for_each(|i| {
                    let y = (self.state[i] & upper_mask) | (self.state[i+1] & lower_mask);
                    self.state[i] = self.state[j] ^ (y >> 1) ^ (if (y & 0x1) > 0 {self.xor_mask} else {0});
                            j += 1;
                });
                
                let y = (self.state[n] & upper_mask) | (self.state[0] & lower_mask);
                self.state[n] = self.state[(self.shift_size as usize)- 1] ^ (y >> 1) ^ 
                    (if (y & 0x1) > 0 {self.xor_mask} else {0});
                self.idx = 0;
            }
        }

        impl Source<$Type0> for MersenneTwisterRand<$Type0> {
            fn gen(&mut self) -> Result<$Type0> {
                self.check_init();
                
                if self.idx >= self.state_size {
                    self.gen_rand();
                }
                let mut z = self.state[self.idx as usize];
                z ^= (z >> self.tempering_u) & self.tempering_d;
                z ^= (z >> self.tempering_s) & self.tempering_b;
                z ^= (z >> self.tempering_t) & self.tempering_c;
                z ^= z >> self.shift_l;
                
                self.idx += 1;
                Ok(z)
            }

            fn reset<Sd: Seed<$Type0>>(&mut self, sd: &Sd) -> Result<()> {
                sd.seed().map(|x| {
                    self.seed = Err(x);
                    self.check_init();
                })
            }
        }
    };
}

mtr_impl!(u32);
mtr_impl!(usize);
mtr_impl!(u64);

/// 32-bit Mersenne Twister by Matsumoto and Nishimura, 1998
#[macro_export]
macro_rules! mt19937 {
    ($Sd: ident) => {
        rmath::rand::MersenneTwisterRand::new(&$Sd, 32u32, 624u32, 397u32, 31u32, 0x9908b0dfu32, 
                (11u32, 0xffffffffu32), (7u32, 0x9d2c5680u32), (15u32, 0xefc60000u32),
                 18u32, 1812433253u32)
    };
}


/// 64-bit Mersenne Twister by Matsumoto and Nishimura, 2000
#[macro_export]
macro_rules! mt19937_64 {
    ($Sd: ident) => {
        rmath::rand::MersenneTwisterRand::new(&$Sd, 64u64, 312u64, 156u64, 31u64, 0xb5026f5aa96619e9u64, 
                (29u64, 0x5555555555555555u64), (17u64, 0x71d67fffeda60000u64), (37u64, 0xfff7eee000000000u64),
                 43u64, 6364136223846793005u64)
    };
}