double-double
Version:
Pure double-double precision functions *with strict error bounds*.
33 lines (32 loc) • 1.27 kB
TypeScript
/**
* Returns the product of a double-double-precision floating point number and a
* double.
*
* * slower than ALGORITHM 8 (one call to fastTwoSum more) but about 2x more
* accurate
* * relative error bound: 1.5u^2 + 4u^3, i.e. fl(a+b) = (a+b)(1+ϵ),
* where ϵ <= 1.5u^2 + 4u^3, u = 0.5 * Number.EPSILON
* * the bound is very sharp
* * probably prefer `ddMultDouble2` due to extra speed
*
* * ALGORITHM 7 of https://hal.archives-ouvertes.fr/hal-01351529v3/document
* @param y a double
* @param x a double-double precision floating point number
*/
declare function ddMultDouble1(y: number, x: number[]): number[];
/**
* Returns the product of a double-double-precision floating point number and a double.
*
* * faster than ALGORITHM 7 (one call to fastTwoSum less) but about 2x less
* accurate
* * relative error bound: 3u^2, i.e. fl(a*b) = (a*b)(1+ϵ),
* where ϵ <= 3u^2, u = 0.5 * Number.EPSILON
* * the bound is sharp
* * probably prefer this algorithm due to extra speed
*
* * ALGORITHM 8 of https://hal.archives-ouvertes.fr/hal-01351529v3/document
* @param y a double
* @param x a double-double precision floating point number
*/
declare function ddMultDouble2(y: number, x: number[]): number[];
export { ddMultDouble1, ddMultDouble2 };