numeric-loops 0.1.1

Efficient numerical loops (sum, dot product) with optional nightly-using special cases and optimizations.
Documentation 
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// Copyright 2014-2016 bluss and ndarray developers.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.

use num_traits::Zero;

use std::cmp;
use std::ops::{
    Add,
    Mul,
};

/// Compute the sum of the values in `xs`
pub fn sum<A>(mut xs: &[A]) -> A
    where A: Clone + Add<Output=A> + Zero,
{
    // eightfold unrolled so that floating point can be vectorized
    // (even with strict floating point accuracy semantics)
    let mut sum = A::zero();
    let (mut p0, mut p1, mut p2, mut p3,
         mut p4, mut p5, mut p6, mut p7) =
        (A::zero(), A::zero(), A::zero(), A::zero(),
         A::zero(), A::zero(), A::zero(), A::zero());
    while xs.len() >= 8 {
        p0 = p0 + xs[0].clone();
        p1 = p1 + xs[1].clone();
        p2 = p2 + xs[2].clone();
        p3 = p3 + xs[3].clone();
        p4 = p4 + xs[4].clone();
        p5 = p5 + xs[5].clone();
        p6 = p6 + xs[6].clone();
        p7 = p7 + xs[7].clone();

        xs = &xs[8..];
    }
    sum = sum.clone() + (p0 + p4);
    sum = sum.clone() + (p1 + p5);
    sum = sum.clone() + (p2 + p6);
    sum = sum.clone() + (p3 + p7);

    // make it clear to the optimizer that this loop is short
    // and can not be autovectorized.
    for i in 0..xs.len() {
        if i >= 7 { break; }
        sum = sum.clone() + xs[i].clone()
    }
    sum
}

/// Compute the dot product.
///
/// `xs` and `ys` must be the same length
pub fn dot<A>(xs: &[A], ys: &[A]) -> A
    where A: Add<Output=A> + Mul<Output=A> + Zero + Copy,
{
    debug_assert_eq!(xs.len(), ys.len());
    // eightfold unrolled so that floating point can be vectorized
    // (even with strict floating point accuracy semantics)
    let len = cmp::min(xs.len(), ys.len());
    let mut xs = &xs[..len];
    let mut ys = &ys[..len];
    let mut sum = A::zero();
    let (mut p0, mut p1, mut p2, mut p3,
         mut p4, mut p5, mut p6, mut p7) =
        (A::zero(), A::zero(), A::zero(), A::zero(),
         A::zero(), A::zero(), A::zero(), A::zero());
    while xs.len() >= 8 {
        p0 = p0 + xs[0] * ys[0];
        p1 = p1 + xs[1] * ys[1];
        p2 = p2 + xs[2] * ys[2];
        p3 = p3 + xs[3] * ys[3];
        p4 = p4 + xs[4] * ys[4];
        p5 = p5 + xs[5] * ys[5];
        p6 = p6 + xs[6] * ys[6];
        p7 = p7 + xs[7] * ys[7];

        xs = &xs[8..];
        ys = &ys[8..];
    }
    sum = sum + (p0 + p4);
    sum = sum + (p1 + p5);
    sum = sum + (p2 + p6);
    sum = sum + (p3 + p7);

    for i in 0..xs.len() {
        if i >= 7 { break; }
        unsafe {
            // get_unchecked is needed to avoid the bounds check
            sum = sum + xs[i] * *ys.get_unchecked(i);
        }
    }
    sum
}