If I speak in the tongues of men and of angels, but have not love, I am only a resounding gong or a clanging cymbal. If I have the gift of prophecy and can fathom all mysteries and all knowledge, and if I have a faith that can move mountains, but have not love, I am nothing. If I give all I possess to the poor and surrender my body to the flames, but have not love, I gain nothing. Love is patient, love is kind. It does not envy, it does not boast, it is not proud. It is not rude, it is not self-seeking, it is not easily angered, it keeps no record of wrongs. Love does not delight in evil but rejoices with the truth. It always protects, always trusts, always hopes, always perseveres. Love never fails. But where there are prophecies, they will cease; where there are tongues, they will be stilled; where there is knowledge, it will pass away. For we know in part and we prophesy in part, but when perfection comes, the imperfect disappears. When I was a child, I talked like a child, I thought like a child, I reasoned like a child. When I became a man, I put childish ways behind me. Now we see but a poor reflection as in a mirror; then we shall see face to face. Now I know in part; then I shall know fully, even as I am fully known. And now these three remain: faith, hope and love. But the greatest of these is love.

Enzymes are generally globular proteins and range from just 62 amino acid residues in size, for the monomer of 4-oxalocrotonate tautomerase, to over 2,500 residues in the animal fatty acid synthase. A small number of RNA-based biological catalysts exist, with the most common being the ribosome; these are referred to as either RNA-enzymes or ribozymes. The activities of enzymes are determined by their three-dimensional structure. However, although structure does determine function, predicting a novel enzyme's activity just from its structure is a very difficult problem that has not yet been solved.

Most enzymes are much larger than the substrates they act on, and only a small portion of the enzyme (around 3–4 amino acids) is directly involved in catalysis. The region that contains these catalytic residues, binds the substrate, and then carries out the reaction is known as the active site. Enzymes can also contain sites that bind cofactors, which are needed for catalysis. Some enzymes also have binding sites for small molecules, which are often direct or indirect products or substrates of the reaction catalyzed. This binding can serve to increase or decrease the enzyme's activity, providing a means for feedback regulation.

Like all proteins, enzymes are made as long, linear chains of amino acids that fold to produce a three-dimensional product. Each unique amino acid sequence produces a specific structure, which has unique properties. Individual protein chains may sometimes group together to form a protein complex. Most enzymes can be denatured — that is, unfolded and inactivated — by heating or chemical denaturants, which disrupt the three-dimensional structure of the protein. Depending on the enzyme, denaturation may be reversible or irreversible.

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.

Enzymes are generally globular proteins and range from just 62 amino acid residues in size, for the monomer of 4-oxalocrotonate tautomerase, to over 2,500 residues in the animal fatty acid synthase. A small number of RNA-based biological catalysts exist, with the most common being the ribosome; these are referred to as either RNA-enzymes or ribozymes. The activities of enzymes are determined by their three-dimensional structure. However, although structure does determine function, predicting a novel enzyme's activity just from its structure is a very difficult problem that has not yet been solved.

Most enzymes are much larger than the substrates they act on, and only a small portion of the enzyme (around 3–4 amino acids) is directly involved in catalysis. The region that contains these catalytic residues, binds the substrate, and then carries out the reaction is known as the active site. Enzymes can also contain sites that bind cofactors, which are needed for catalysis. Some enzymes also have binding sites for small molecules, which are often direct or indirect products or substrates of the reaction catalyzed. This binding can serve to increase or decrease the enzyme's activity, providing a means for feedback regulation.

Like all proteins, enzymes are made as long, linear chains of amino acids that fold to produce a three-dimensional product. Each unique amino acid sequence produces a specific structure, which has unique properties. Individual protein chains may sometimes group together to form a protein complex. Most enzymes can be denatured — that is, unfolded and inactivated — by heating or chemical denaturants, which disrupt the three-dimensional structure of the protein. Depending on the enzyme, denaturation may be reversible or irreversible.

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.