Fixed-point arithmetic

In computing, a fixed-point number representation is a real data type for a number that has a fixed number of digits after (and sometimes also before) the radix point (after the decimal point '.' in English decimal notation). Fixed-point number representation can be compared to the more complicated (and more computationally demanding) floating-point number representation.

Fixed-point numbers are useful for representing fractional values, usually in base 2 or base 10, when the executing processor has no floating point unit (FPU) or if fixed-point provides improved performance or accuracy for the application at hand. Most low-cost embedded microprocessors and microcontrollers do not have an FPU.

Representation

A value of a fixed-point data type is essentially an integer that is scaled by an implicit specific factor determined by the type. For example, the value 1.23 can be represented as 1230 in a fixed-point data type with scaling factor of 1/1000, and the value 1,230,000 can be represented as 1230 with a scaling factor of 1000. Unlike floating-point data types, the scaling factor is the same for all values of the same type, and does not change during the entire computation.

American football rules

Game play in American football consists of a series of downs, individual plays of short duration, outside of which the ball is dead or not in play. These can be plays from scrimmage – passes, runs, punts, or field goal attempts (from either a place kick or a drop kick) – or free kicks such as kickoffs and fair catch kicks. Substitutions can be made between downs, which allows for a great deal of specialization as coaches choose the players best suited for each particular situation. During a play, each team should have no more than 11 players on the field, and each of them has specific tasks assigned for that specific play.

Objective of the game

The objective of this game is to score more points than the other team during the alotted time. The team with the ball (the offense) has 4 plays (downs) to advance at least 10 yards, and can score points once they reach the opposite end of the field, which is home to a scoring zone called the end zone, as well as the goal posts. If the offense succeeds in advancing at least 10 yards, they earn a "first down" and the number of tries allotted is reset and they are again given 4 tries to advance an additional 10 yards, starting from the spot to which they last advanced. If the offense does not advance at least 10 yards during their 4 downs, the team without the ball (the defense) regains control of the ball (called turnover on downs).

Point (mortgage)

Points, sometimes also called "discount points", are a form of pre-paid interest. One point equals one percent of the loan amount. By charging a borrower points, a lender effectively increases the yield on the loan above the amount of the stated interest rate. Borrowers can offer to pay a lender points as a method to reduce the interest rate on the loan, thus obtaining a lower monthly payment in exchange for this up-front payment. In United States, for each point purchased, the loan rate is typically reduced by anywhere from 1/8% (0.125%) to 1/4% (0.25%).

Selling the property or refinancing prior to this break-even point will result in a net financial loss for the buyer while keeping the loan for longer than this break-even point will result in a net financial savings for the buyer. The longer you keep the property financed under the loan with purchased points, the more the money spent on the points will pay off. Accordingly, if the intention is to buy and sell the property or refinance in a rapid fashion, paying points is actually going to end up costing more than just paying the loan at the higher interest rate.

Point (ice hockey)

In ice hockey, point has three contemporary meanings:

Flip (mathematics)

In algebraic geometry, flips and flops are codimension-2 surgery operations arising in the minimal model program, given by blowing up along a relative canonical ring. In dimension 3 flips are used to construct minimal models, and any two birationally equivalent minimal models are connected by a sequence of flops. It is conjectured that the same is true in higher dimensions.

The minimal model program

The minimal model program can be summarised very briefly as follows: given a variety , we construct a sequence of contractions , each of which contracts some curves on which the canonical divisor is negative. Eventually, should become nef (at least in the case of nonnegative Kodaira dimension), which is the desired result. The major technical problem is that, at some stage, the variety may become 'too singular', in the sense that the canonical divisor is no longer Cartier, so the intersection number with a curve is not even defined.

The (conjectural) solution to this problem is the flip. Given a problematic as above, the flip of is a birational map (in fact an isomorphism in codimension 1) to a variety whose singularities are 'better' than those of . So we can put , and continue the process.

Fixed (typeface)

misc-fixed is a collection of monospace bitmap fonts that is distributed with the X Window System. It is a set of independent bitmap fonts which—apart from all being sans-serif fonts—cannot be described as belonging to a single font family. The misc-fixed fonts were the first fonts available for the X Window System. Their individual origin is not attributed, but it is likely that many of them were created in the early or mid 1980s as part of MIT's Project Athena, or at its industrial partner, DEC. The misc-fixed fonts are available under a "public domain – share and enjoy" licence.

The individual fonts in the collection have a short name that matches their respective pixel dimensions, plus a letter that indicates a bold or oblique variant. They can also be accessed using their (much longer) X Logical Font Description string:

The "6x13" font is usually also available under the alias "fixed", a font name that is expected to be available on every X server.

The fonts originally covered only the ASCII repertoire, and were in the early 1990s extended to cover all characters in ISO 8859-1. In 1997, Markus Kuhn initiated and headed a project to extend the misc-fixed fonts to as large a subset of Unicode/ISO 10646 as is feasible for each of the available font sizes. This project's goal was to get GNU/Linux developers interested in abandoning the 1990s dominant ISO 8859-1 encoding, in favour of using UTF-8 instead, which happened indeed within a few years. Thanks to this effort, all the misc fixed fonts now cover the characters found in