double-double
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Pure double-double precision functions *with strict error bounds*.
38 lines • 1.24 kB
JavaScript
/**
* Returns the result of subtracting the second given double-double-precision
* floating point number from the first.
*
* * relative error bound: 3u^2 + 13u^3, i.e. fl(a-b) = (a-b)(1+ϵ),
* where ϵ <= 3u^2 + 13u^3, u = 0.5 * Number.EPSILON
* * the error bound is not sharp - the worst case that could be found by the
* authors were 2.25u^2
*
* ALGORITHM 6 of https://hal.archives-ouvertes.fr/hal-01351529v3/document
* @param x a double-double precision floating point number
* @param y another double-double precision floating point number
*/
function ddDiffDd(x, y) {
const xl = x[0];
const xh = x[1];
const yl = y[0];
const yh = y[1];
//const [sl,sh] = twoSum(xh,yh);
const sh = xh - yh;
const _1 = sh - xh;
const sl = (xh - (sh - _1)) + (-yh - _1);
//const [tl,th] = twoSum(xl,yl);
const th = xl - yl;
const _2 = th - xl;
const tl = (xl - (th - _2)) + (-yl - _2);
const c = sl + th;
//const [vl,vh] = fastTwoSum(sh,c)
const vh = sh + c;
const vl = c - (vh - sh);
const w = tl + vl;
//const [zl,zh] = fastTwoSum(vh,w)
const zh = vh + w;
const zl = w - (zh - vh);
return [zl, zh];
}
export { ddDiffDd };
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