rmath 0.1.5

A rust math library
Documentation 
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//! this is convert from the golang source code.
//! 
//! 
//! test nat_sqr              ... bench:      13,988 ns/iter (+/- 1,483)
//! test nat_sqr_by_pow       ... bench:      25,861 ns/iter (+/- 3,706)
//! test nat_pow_mod_by_exp   ... bench:   4,120,850 ns/iter (+/- 272,778)
//! test nat_mul_by_karatsuba ... bench:     282,316 ns/iter (+/- 36,541)

#![allow(unused)]

/// z = x*y   
/// (z >> 32, z & 0xffffffff)  
#[inline]
pub(super) fn mul_ww(x: u32, y: u32) -> (u32, u32) {
    let z = (x as u64) * (y as u64);
    ((z >> 32) as u32, (z & 0xffffffff) as u32)
}

/// z = x*y + c   
/// (z >> 32, z & 0xffffffff)  
#[inline]
pub(super) fn mul_add_www(x: u32, y: u32, c: u32) -> (u32, u32) {
    let z = ((x as u64) * (y as u64)) + (c as u64);
    ((z >> 32) as u32, (z & 0xffffffff) as u32)
}

/// (q, r)  
/// q = ((u1 << 32) + u0 - r) / v
/// 
/// # panics
/// 
/// v == 0 or v <= u1
#[inline]
pub(super) fn div_ww(u1: u32, u0: u32, v: u32) -> (u32, u32) {
    let z = ((u1 as u64) << 32) + (u0 as u64);
    let v = v as u64;
    ((z / v) as u32, (z % v) as u32)
}

/// z = x + y   
/// return carry   
pub(super) fn add_vv(z: &mut [u32], x: &[u32], y: &[u32]) -> u32 {
    z.iter_mut().zip(x.iter().zip(y.iter())).fold(0, |c, (zt, (&xt, &yt))| {
        let (tt0, cc0) = xt.overflowing_add(yt);
        let (tt, cc) = tt0.overflowing_add(c);
        *zt = tt;
        if cc0 || cc {1} else {0}
    })
}

pub(super) unsafe fn add_vv_inner(z: *mut u32, x: *const u32, y: *const u32, n: usize) -> u32 {
    (0..n).fold(0, |c, i| {
        let (tt0, cc0) = x.add(i).read().overflowing_add(y.add(i).read());
        let (tt, cc) = tt0.overflowing_add(c);
        z.add(i).write(tt);
        if cc0 || cc {1} else {0}
    })
}

/// z = x - y   
/// return carry   
pub(super) fn sub_vv(z: &mut [u32], x: &[u32], y: &[u32]) -> u32 {
    z.iter_mut().zip(x.iter().zip(y.iter())).fold(0, |c, (zt, (&xt, &yt))| {
        let (tt0, cc0) = xt.overflowing_sub(yt);
        let (tt, cc) = tt0.overflowing_sub(c);
        *zt = tt;
        if cc0 || cc {1} else {0}
    })
}

pub(super) unsafe fn sub_vv_inner(z: *mut u32, x: *const u32, y: *const u32, n: usize) -> u32 {
    (0..n).fold(0, |c, i| {
        let (tt0, cc0) = x.add(i).read().overflowing_sub(y.add(i).read());
        let (tt, cc) = tt0.overflowing_sub(c);
        z.add(i).write(tt);
        if cc0 || cc {1} else {0}
    })
}

pub(super) fn add_vw(z: &mut [u32], x: &[u32], y: u32) -> u32 {
    z.iter_mut().zip(x.iter()).fold(y, |c, (zt, &xt)| {
        let (tt, cc) = xt.overflowing_add(c);
        *zt = tt;
        if cc {1} else {0}
    })
}

pub(super) unsafe fn add_vw_inner(z: *mut u32, x: *const u32, y: u32, n: usize) -> u32 {
    (0..n).fold(y, |c, i|{
        let (tt, cc) = x.add(i).read().overflowing_add(c);
        z.add(i).write(tt);
        if cc {1} else {0}
    })
}

pub(super) fn add_vw_large(z: &mut [u32], x: &[u32], y: u32) -> u32 {
    z.iter_mut().zip(x.iter()).fold(y, |c, (zt, &xt)| {
        if c == 0 {
            *zt = xt;
            0
        } else {
            let (tt, cc) = xt.overflowing_add(c);
            *zt = tt;
            if cc {1} else {0}
        }
    })
}

pub(super) fn sub_vw(z: &mut [u32], x: &[u32], y: u32) -> u32 {
    z.iter_mut().zip(x.iter()).fold(y, |c, (zt, &xt)| {
        let (tt, cc) = xt.overflowing_sub(c);
        *zt = tt;
        if cc {1} else {0}
    })
}

pub(super) unsafe fn sub_vw_inner(z: *mut u32, x: *const u32, y: u32, n: usize) -> u32 {
    (0..n).fold(y, |c, i|{
        let (tt, cc) = x.add(i).read().overflowing_sub(c);
        z.add(i).write(tt);
        if cc {1} else {0}
    })
}

pub(super) fn sub_vw_large(z: &mut [u32], x: &[u32], y: u32) -> u32 {
    z.iter_mut().zip(x.iter()).fold(y, |c, (zt, &xt)| {
        if c == 0 {
            *zt = xt;
            0
        } else {
            let (tt, cc) = xt.overflowing_sub(c);
            *zt = tt;
            if cc {1} else {0}
        }
    })
}

pub(super) fn shl_vu(z: &mut [u32], x: &[u32], s: usize) -> u32 {
    if s == 0 || x.is_empty(){
        z.copy_from_slice(x);
        return 0;
    }
    
    let s = s & 31;
    let ss = (32 - s) & 31;
    let c = x.last().unwrap() >> s;
    x.iter().rev().skip(1).zip(x.iter().rev().zip(z.iter_mut().rev())).for_each(|(&xt0, (&xt1, zt))| {
        *zt = (xt1 << s) | (xt0 >> ss);
    });
    z[0] = x[0] << s;
    c
}

pub(super) unsafe fn shl_vu_inner(z: *mut u32, x: *const u32, s: usize, n: usize) -> u32 {
    if s == 0 || n == 0 {
        std::ptr::copy(x, z, n);
        return 0;
    }
    
    let s = s & 31;
    let ss = (32-s) & 31;
    let c= x.add(n-1).read() >> ss;
    for i in (1..n).rev() {
        z.add(i).write((x.add(i).read() << s) | (x.add(i-1).read() >> ss));
    }
    z.write(x.read() << s);
    c
}

pub(super) fn shr_vu(z: &mut [u32], x: &[u32], s: usize) -> u32 {
    if s == 0 || x.is_empty(){
        z.copy_from_slice(x);
        return 0;
    }
    let s = s & 31;
    let ss = (32 - s) & 31;
    let c = x[0] << ss;
    x.iter().skip(1).zip(x.iter().zip(z.iter_mut())).for_each(|(&xt1, (&xt0, zt))| {
        *zt = (xt0 >> s) | (xt1 << ss);
    });
    *z.last_mut().unwrap() = x.last().unwrap() >> s;
    c
}

pub(super) unsafe fn shr_vu_inner(z: *mut u32, x: *const u32, s: usize, n: usize) -> u32 {
    if s == 0 || n == 0 {
        std::ptr::copy(x, z, n);
        return 0;
    }
    
    let s = s & 31;
    let ss = (32 - s) & 31;
    let c = x.read() << ss;
    for i in 0..(n-1) {
        let tmp = (x.add(i).read() >> s) | (x.add(i+1).read() << ss);
        z.add(i).write(tmp);
    }
    z.add(n-1).write(x.add(n-1).read() >> s);
    c
}

pub(super) fn mul_add_vww(z: &mut [u32], x: &[u32], y: u32, r: u32) -> u32 {
    z.iter_mut().zip(x.iter()).fold(r, |c, (zt, &xt)| {
        let (cc, tt) = mul_add_www(xt, y, c);
        *zt = tt;
        cc
    })
}

/// z = x*y + z
pub(super) fn add_mul_vvw(z: &mut [u32], x: &[u32], y: u32) -> u32 {
    z.iter_mut().zip(x.iter()).fold(0, |c, (zt, &xt)| {
        let (z1, z0) = mul_add_www(xt, y, *zt);
        let (lo, cc) = z0.overflowing_add(c);
        *zt = lo;
        if cc {1 + z1} else {z1}
    })
}

pub(super) unsafe fn add_mul_vvw_inner(z: *mut u32, x: *const u32, y: u32, n: usize) -> u32{
    (0..n).fold(0, |c, i| {
        let (z1, z0) = mul_add_www(x.add(i).read(), y, z.add(i).read());
        let (lo, cc) = z0.overflowing_add(c);
        z.add(i).write(lo);
        if cc {1 + z1} else {z1}
    })
}

pub(super) fn div_wvw(z: &mut [u32], xn: u32, x: &[u32], y: u32) -> u32 {
    z.iter_mut().zip(x.iter()).fold(xn, |r, (zt, &xt)| {
        let (tmpz, tmpr) = div_ww(r, xt, y);
        *zt = tmpz;
        tmpr
    })
}