The underlying causes leading to the crisis had been reported in business journals for many months before September 2008, with commentary about the financial stability of leading U.S. and European investment banks, insurance firms and mortgage banks consequent to the subprime mortgage crisis.

Beginning with failures caused by misapplication of risk controls for bad debts, collateralization of debt insurance and fraud, large financial institutions in the United States and Europe faced a credit crisis and a slowdown in economic activity. The impacts rapidly developed and spread into a global shock resulting in a number of European bank failures and declines in various stock indexes, and large reductions in the market value of equities and commodities. The credit crisis was exacerbated by Section 128 of the US Emergency Economic Stabilization Act of 2008 which allowed the Federal Reserve to pay interest on excess reserve requirement balances held on deposit from banks, removing the incentive for banks to extend credit instead of placing cash on deposit with the Fed. Moreover, the de-leveraging of financial institutions further accelerated the liquidity crisis and caused a decrease in international trade. World political leaders, national ministers of finance and central bank directors coordinated their efforts to reduce fears, but the crisis continued. At the end of October a currency crisis developed, with investors transferring vast capital resources into stronger currencies such as the yen, the dollar and the Swiss franc, leading many emergent economies to seek aid from the International Monetary Fund.

Internet Protocol version 6 (IPv6) is the next-generation Internet Layer protocol for packet-switched internetworks and the Internet. IPv4 is currently the dominant Internet Protocol version, and was the first to receive widespread use. In December 1998, the Internet Engineering Task Force (IETF) designated IPv6 as the successor to version 4 by the publication of a Standards Track specification, RFC 2460.

In December 2008, despite celebrating its 10th anniversary as a Standards Track protocol, IPv6 was only in its infancy in terms of general worldwide deployment. A recent study by Google indicates that penetration is still less than one percent of Internet traffic in any country. The leaders are Russia (0.76%), France (0.65%), Ukraine (0.64%), Norway (0.49%), and the United States (0.45%). Although Asia leads in terms of absolute deployment numbers, the relative penetration is smaller (e.g., China: 0.24%). IPv6 is implemented on all major operating systems in use in commercial, business, and home consumer environments. According to the study, Mac OS X leads in IPv6 penetration of 2.44%, followed by Linux (0.93%) and Windows Vista (0.32%).

IPv6 has a much larger address space than IPv4. This results from the use of a 128-bit address, where IPv4 uses only 32 bits. The new address space thus supports 2^128 (about 3.4×10^38) addresses. This expansion provides flexibility in allocating addresses and routing traffic and eliminates the need for network address translation (NAT). NAT gained widespread deployment as an effort to alleviate IPv4 address exhaustion.

IPv6 also implements new features that simplify aspects of address assignment (stateless address autoconfiguration) and network renumbering (prefix and router announcements) when changing Internet connectivity providers. The IPv6 subnet size has been standardized by fixing the size of the host identifier portion of an address to 64 bits to facilitate an automatic mechanism for forming the host identifier from Link Layer media addressing information (MAC address).

Network security is integrated into the design of the IPv6 architecture. Internet Protocol Security (IPsec) was originally developed for IPv6, but found widespread optional deployment first in IPv4 (into which it was back-engineered). The IPv6 specifications mandate IPsec implementation as a fundamental interoperability requirement.

The general requirements for implementing IPv6 on a network host are specified in RFC 4294.

The United States and China hold the best hope for leading a global economic recovery, yet they may lack sufficient strength to firmly pull the world out of recession.

President Barack Obama warned fellow world leaders at the Group of 20 summit in London that they should not count on "voracious" U.S. consumers generating the level of demand that helped drive eight years of strong global economic growth.

But without an obvious growth engine to replace flagging American consumption, the global economy appears headed for a prolonged slump followed by only a tepid rebound.

"It is going to be a difficult paradox for the world, with the economy at the epicenter of the crisis -- the United States -- still being seen as the savior of the world at large," said Eswar Prasad, a senior fellow at the Brookings Institution.

"You are Israel's teacher," said Jesus, "and do you not understand these things? I tell you the truth, we speak of what we know, and we testify to what we have seen, but still you people do not accept our testimony. I have spoken to you of earthly things and you do not believe; how then will you believe if I speak of heavenly things? No one has ever gone into heaven except the one who came from heaven—the Son of Man. Just as Moses lifted up the snake in the desert, so the Son of Man must be lifted up, that everyone who believes in him may have eternal life. "For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. For God did not send his Son into the world to condemn the world, but to save the world through him. Whoever believes in him is not condemned, but whoever does not believe stands condemned already because he has not believed in the name of God's one and only Son. This is the verdict: Light has come into the world, but men loved darkness instead of light because their deeds were evil. Everyone who does evil hates the light, and will not come into the light for fear that his deeds will be exposed. But whoever lives by the truth comes into the light, so that it may be seen plainly that what he has done has been done through God."

The Democratic-controlled U.S. Congress on Thursday approved budget blueprints embracing President Barack Obama's agenda but leaving many hard choices until later and a government deeply in the red.

With no Republican support, the House of Representatives and Senate approved slightly different, less expensive versions of Obama's $3.55 trillion budget plan for fiscal 2010, which begins on October 1. The differences will be worked out over the next few weeks.

Obama, who took office in January after eight years of the Republican Bush presidency, has said the Democrats' budget is critical to turning around the recession-hit U.S. economy and paving the way for sweeping healthcare, climate change and education reforms he hopes to push through Congress this year.

Obama, traveling in Europe, issued a statement praising the votes as "an important step toward rebuilding our struggling economy." Vice President Joe Biden, who serves as president of the Senate, presided over that chamber's vote.

Builders of computer systems often need information about floating-point arithmetic. There are, however, remarkably few sources of detailed information about it. One of the few books on the subject, Floating-Point Computation by Pat Sterbenz, is long out of print. This paper is a tutorial on those aspects of floating-point arithmetic (floating-point hereafter) that have a direct connection to systems building. It consists of three loosely connected parts. The first Section, "Rounding Error," on page 173, discusses the implications of using different rounding strategies for the basic operations of addition, subtraction, multiplication and division. It also contains background information on the two methods of measuring rounding error, ulps and relative error. The second part discuses the IEEE floating-point standard, which is becoming rapidly accepted by commercial hardware manufacturers. Included in the IEEE standard is the rounding method for basic operations. The discussion of the standard draws on the material in the Section , "Rounding Error," on page 173. The third part discusses the onnections between floating-point and the design of various aspects of computer systems. Topics include instruction set design, optimizing compilers and exception handling.

I have tried to avoid making statements about floating-point without also giving reasons why the statements are true, especially since the justifications involve nothing more complicated than elementary calculus. Those explanations that are not central to the main argument have been grouped into a section called "The Details," so that they can be skipped if desired. In particular, the proofs of many of the theorems appear in this section. The end of each proof is marked with the * symbol; when a proof is not included, the * appears immediately following the statement of the theorem.

Squeezing infinitely many real numbers into a finite number of bits requires an approximate representation. Although there are infinitely many integers, in most programs the result of integer computations can be stored in 32 bits. In contrast, given any fixed number of bits, most calculations with real numbers will produce quantities that cannot be exactly represented using that many bits. Therefore the result of a floating-point calculation must often be rounded in order to fit back into its finite representation. This rounding error is the characteristic feature of floating-point computation. "Relative Error and Ulps" on page 176 describes how it is measured.

Since most floating-point calculations have rounding error anyway, does it matter if the basic arithmetic operations introduce a little bit more rounding error than necessary? That question is a main theme throughout this section. "Guard Digits" on page 178 discusses guard digits, a means of reducing the error when subtracting two nearby numbers. Guard digits were considered sufficiently important by IBM that in 1968 it added a guard digit to the double precision format in the System/360 architecture (single precision already had a guard digit), and retrofitted all existing machines in the field. Two examples are given to illustrate the utility of guard digits.

The IEEE standard goes further than just requiring the use of a guard digit. It gives an algorithm for addition, subtraction, multiplication, division and square root, and requires that implementations produce the same result as that algorithm. Thus, when a program is moved from one machine to another, the results of the basic operations will be the same in every bit if both machines support the IEEE standard. This greatly simplifies the porting of programs. Other uses of this precise specification are given in "Exactly Rounded Operations" on page 185.