The markets rewarded Apple and Google Tuesday after reports that activations of new iOS and Android devices surged over the weekend that included Christmas.

At the close, Apple shares were up nearly 1 percent to $406.53 while Google shares rose 1.1 percent to $640.25 as the S&P 500 also inched up slightly to 1,265.43 after rising about 1 percent at midday.

Localytics, a Boston market researcher, reported new activations of iOS and Android devices surged 12 times over previous weekends, an obvious indication that iPods, iPads, iPhones and Android devices were extensively given as holuday gifts.

There was a huge increase, Localytics said, compared to new activations the past four weekends, with the highest traffic in the U.S. and Germany.

The researcher registered 12.5 times as many iOS devices in the period; 21 times more iPods were noted in the U.S., along with 14 times more iPhones. The company didn't break out new iPhone 3, iPhone 4 and iPhone 4S models.

Android, the OS developed by Mountain View, Calif.-based Google, also saw 12 times more activations, Localytics reported. The strongest growth was in South Korea (up 80 percent), followed by Sweden and Japan. The pattern illustrates strong demand for phones and tablets from Apple competitors such as Samsung Electronics, Sony, HTC and others.

Cupertino, Calif.-based Apple, once close to Google, is now in a bitter rivalry over software. By early 2012, Google expects to complete its $12.5 billion acquisition of Motorola Mobility, of Libertyville, Il., to move squarely into the smartphone and tablet hardware sector.