src/lib/math/hypot.go

// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package math

/*
 *	hypot -- sqrt(p*p + q*q), but overflows only if the result does.
 *	See Cleve Moler and Donald Morrison,
 *	Replacing Square Roots by Pythagorean Sums
 *	IBM Journal of Research and Development,
 *	Vol. 27, Number 6, pp. 577-581, Nov. 1983
 */

// Hypot computes Sqrt(p*p + q*q), taking care to avoid
// unnecessary overflow and underflow.
func Hypot(p, q float64) float64 {
	if p < 0 {
		p = -p;
	}
	if q < 0 {
		q = -q;
	}

	if p < q {
		p, q = q, p;
	}

	if p == 0 {
		return 0;
	}

	pfac := p;
	q = q/p;
	r := q;
	p = 1;
	for {
		r = r*r;
		s := r+4;
		if s == 4 {
			return p*pfac;
		}
		r = r/s;
		p = p + 2*r*p;
		q = q*r;
		r = q/p;
	}
	panic("unreachable")
}