the-french-artist/wikipedia_20220301.simple_sentence_embeddings huggingface dataset:
Rounding 
 This enhancement is frequently used in image and audio processing (notably for accurate rescaling and antialiasing operations, where the simple probabilistic dithering of isolated values may still produce perceptible noise, sometimes even worse than the moiré effects occurring with simple non-probabilistic rounding methods applied to isolated samples).
Rounding 
 The effective propagation of accumulated roundoff errors may depend on the discrete dimension of the sampled data to round: when sampling bidimensional images, including colored images (that add the discrete dimension of color planes), or tridimensional videos (that add a discrete time dimension), or on polyphonic audio data (using time and channel discrete dimensions), it may still be preferable to propagate this error into a preferred direction, or equally into several orthogonal dimensions, such as vertically vs. horizontally for bidimensional images, or into parallel color channels at the same position and/or timestamp, and depending on other properties of these orthogonal discrete dimensions (according to a perception model).
Rounding 
 In those cases, several roundoff error accumulators may be used (at least one for each discrete dimension), or a (n-1)-dimension vector (or matrix) of accumulators.
Rounding 
 In some of these cases, the discrete dimensions of the data to sample and round may be treated non orthogonally: for example, when working with colored images, the trichromatic color planes data in each physical dimension (height, width and optionally time) could be remapped using a perceptive color model, so that the roundoff error accumulators will be designed to preserve lightness with a higher probability than hue or saturation, instead of propagating errors into each orthogonal color plane independently; and in stereophonic audio data the two rounded data channels (left and right) may be rounded together to preserve their mean value in priority to their effective difference that will absorb most of the remaining roundoff errors, in a balanced way around zero.
Rounding 
 In some contexts it is desirable to round a given number x to a "neat" fraction — that is, the nearest fraction z = m/n
Rounding 
 This problem is fairly distinct from that of rounding a value to a fixed number of decimal or binary digits, or to a multiple of a given unit m. This problem is related to Farey sequences, the Stern-Brocot tree, and continued fractions.
Rounding 
 This type of rounding, which is also named rounding to a logarithmic scale, is a variant of Rounding to a specified increment but with an increment that is modified depending on the scale and magnitude of the result.
Rounding 
 Concretely, the intent is to limit the number of significant digits, rounding the value so that non-significant digits will be dropped.
Rounding 
 This type of rounding occurs implicitly with numbers computed with floating-point values with limited precision (such as IEEE-754 float and double types), but it may be used more generally to round any real values with any positive number of significant digits and any strictly positive real base.
Rounding 
 For example it can be used in engineering graphics for representing data with a logarithmic scale with variable steps (for example wave lengths, whose base is not necessarily an integer measure), or in statistical data to define classes of real values within intervals of exponentially growing widths (but the most common use is with integer bases such as 10 or 2).
Rounding 
 This type of rounding is based on a logarithmic scale defined by a fixed non-zero real scaling factor s (in most frequent cases this factor is s=1) and a fixed positive base b>1 (not necessarily an integer and most often different from the scaling factor), and a fixed integer number n>0 of significant digits in that base (which will determine the value of the increment to use for rounding, along with the computed effective scale of the rounded number).
Rounding 
 The primary argument number (as well as the resulting rounded number) is first represented in exponential notation x = s·a·m·bc, such that the sign s is either +1 or −1, the absolute mantissa a is restricted to the half-open positive interval [1/b,1), and the exponent c is any (positive or negative) integer.
Rounding 
 In that representation, all significant digits are in the fractional part of the absolute mantissa whose integer part is always zero.
Rounding 
 If the source number (or rounded number) is 0, the absolute mantisssa a is defined as 0, the exponent c is fixed to an arbitrary value (0 in most conventions, but some floating-point representations cannot use a null absolute mantissa but reserve a specific maximum negative value for the exponent c to represent the number 0 itself), and the sign s may be arbitrarily chosen between −1 or +1 (it is generally set to +1 for simple zero, or it is set to the same sign as the argument in the rounded value if the number representation allows to differentiate positive and negative zeroes, even if they finally represent the same numeric value 0).
Rounding 
 A scaled exponential representation as x = a·s·bc may also be used equivalently, with a signed mantissa a either equal to zero or within one of the two half-open intervals (−1,−1/b] and [+1/b,+1), and this will be the case in the algorithm below.
Rounding 
 let the scaling exponent c be one plus the base-b logarithm of the absolute value of x’, rounded down to an integer (towards minus infinity): ;
Rounding 
 let m be the increment for rounding the mantissa a according to the number of significant digits to keep:
Rounding 
 let a’ be the signed mantissa a rounded according to this increment m and the selected rounding mode:
Rounding 
 if the absolute value of a’ is not lower than b, then decrement n (multiply the increment m by b), increment the scaling exponent c’, divide the signed mantissa a by b, and restart the rounding of the new signed mantissa a into a’ with the same formula; this step may be avoided only if the abtract "round()" function is always rounding a towards 0 (i.e. when it is a simple truncation), but is necessary if it may be rounding a towards infinity, because the rounded mantissa may have a higher scaling exponent in this case, leaving an extra digit of precision.
Rounding 
 For the abstract "round()" function, this type of rounding can use any one of the rounding to integer modes described more completely in the next section, but it is most frequently the round to nearest mode (with tie-breaking rules also described more completely below).
Rounding 
 the scaled rounding of 1.234 with scaling factor 1 in base 10 and 3 significant digits (maximum relative precision=1/1000), when using any round to nearest mode, will return 1.23;
Rounding 
 the scaled rounding of 1.234 scaling factor 1 in base 10 and 3 significant digits (maximum relative precision=1/1000), when using the round down mode, will return 1.23;
Rounding 
 the scaled rounding of  with scaling factor  in base 2 and 3 significant digits (maximum relative precision=1/8), when using the round down mode, will return ;
Rounding 
 Finished lumber, writing paper, capacitors, and many other products are usually sold in only a few standard sizes.
Rounding 
 Many design procedures describe how to calculate an approximate value, and then "round" to some standard size using phrases such as "round down to nearest standard value", "round up to nearest standard value", or "round to nearest standard value".
Rounding 
 In floating-point arithmetic, rounding aims to turn a given value x into a value z with a specified number of significant digits.
Rounding 
 In other words, z should be a multiple of a number m that depends on the magnitude of z. The number m is a power of the base (usually 2 or 10) of the floating-point form.
Rounding 
 Apart from this detail, all the variants of rounding discussed above apply to the rounding of floating-point numbers as well.
Rounding 
 The algorithm for such rounding is presented in the Scaled rounding section above, but with a constant scaling factor s=1, and an integer base b>1.
Rounding 
 For results where the rounded result would overflow the result for a directed rounding is either the appropriate signed infinity, or the highest representable positive finite number (or the lowest representable negative finite number if x is negative), depending on the direction of rounding.
Rounding 
 In addition, if the rounded result would underflow, i.e. if the exponent would exceed the lowest representable integer value, the effective result may be either zero (possibly signed if the representation can maintain a distinction of signs for zeroes), or the smallest representable positive finite number (or the highest representable negative finite number if x is negative), possibly a denormal positive or negative number (if the mantissa is storing all its significant digits, in which case the most significant digit may still be stored in a lower position by setting the highest stored digits to zero, and this stored mantissa does not drop the most significant digit, something that is possible when base b=2 because the most significant digit is always 1 in that base), depending on the direction of rounding.
Rounding 
 Rounding a number twice in succession to different precisions, with the latter precision being coarser, is not guaranteed to give the same result as rounding once to the final precision except in the case of directed rounding.
Rounding 
 For instance rounding 9.46 to one decimal gives 9.5, and then 10 when rounding to integer using rounding half to even, but would give 9 when rounded to integer directly.
Rounding 
 Some computer languages and the IEEE 754-2008 standard dictate that in straightforward calculations, the result should not be rounded twice.
Rounding 
 This has been a particular problem with Java as it is designed to be run identically on different machines, special programming tricks have had to be used to achieve this with x87 floating point.
Rounding 
 The Java language was changed to allow different results where the difference does not matter and require a "strictfp" qualifier to be used when the results have to conform accurately.
Rounding 
 It is possible to use rounded arithmetic to evaluate the exact value of a function with a discrete domain and range.
Rounding 
 For example, if we know that an integer n is a perfect square, we can compute its square root by converting n to a floating-point value x, computing the approximate square root y of x with floating point, and then rounding y to the nearest integer q. If n is not too big, the floating-point roundoff error in y will be less than 0.5, so the rounded value q will be the exact square root of n. In most modern computers, this method may be much faster than computing the square root of n by an all-integer algorithm.
Rounding 
 William Kahan coined the term "The Table-Maker's Dilemma" for the unknown cost of rounding transcendental functions:
Rounding 
 "Nobody knows how much it would cost to compute  y^w  correctly rounded for every two floating-point arguments at which it does not over/underflow.
Rounding 
 Instead, reputable math libraries compute elementary transcendental functions mostly within slightly more than half an ulp and almost always well within one ulp.
Rounding 
 Because nobody knows how much computation it would cost... No general way exists to predict how many extra digits will have to be carried to compute a transcendental expression and round it correctly to some preassigned number of digits.
Rounding 
 Even the fact (if true) that a finite number of extra digits will ultimately suffice may be a deep theorem."
Rounding 
 The IEEE floating point standard guarantees that add, subtract, multiply, divide, square root, and floating point remainder will give the correctly rounded result of the infinite precision operation.
Rounding 
 However, no such guarantee is given for more complex functions and they are typically only accurate to within the last bit at best.
Rounding 
 Using the Gelfond–Schneider theorem and Lindemann–Weierstrass theorem, many of the standard elementary functions can be proved to return transcendental results when given rational non-zero arguments; therefore it is always possible to correctly round such functions.
Rounding 
 However determining a limit for a given precision on how accurate results needs to be computed before a correctly rounded result can be guaranteed may demand a lot of computation time.
Rounding 
 IBM has written a package for fast and accurate IEEE elementary functions and in the future the standard libraries may offer such precision.
Rounding 
 It is possible to devise well-defined computable numbers which it may never be possible to correctly round no matter how many digits are calculated.
Rounding 
 For instance, if Goldbach's conjecture is true but unprovable, then it is impossible to correctly round down 0.5 + 10-n where n is the first even number greater than 4 which is not the sum of two primes, or 0.5 if there is no such number.
Rounding 
 Some ancient clay tablets found in Mesopotamia contain tables with rounded values of reciprocals and square roots in base 60.
Rounding 
 In the 1906 4th edition of Probability and Theory of Errors  Robert Simpson Woodward called this "the computer's rule" indicating that it was then in common use by human computers who calculated mathematical tables.
Rounding 
 Churchill Eisenhart's 1947 paper "Effects of Rounding or Grouping Data" (in Selected Techniques of Statistical Analysis, McGrawHill, 1947, Eisenhart, Hastay, and Wallis, editors) indicated that the practice was already "well established" in data analysis.
Rounding 
 If this rounding method was ever a standard in banking, the evidence has proved extremely difficult to find.
Rounding 
 To the contrary, section 2 of the European Commission report The Introduction of the Euro and the Rounding of Currency Amounts  suggests that there had previously been no standard approach to rounding in banking; and it specifies that "half-way" amounts should be rounded up.
Rounding 
 Until the 1980s, the rounding method used in floating-point computer arithmetic was usually fixed by the hardware, poorly documented, inconsistent, and different for each brand and model of computer.
Rounding 
 This situation changed after the IEEE 754 floating point standard was adopted by most computer manufacturers.
Rounding 
 The standard allows the user to choose among several rounding modes, and in each case, specifies precisely how the results should be rounded.
Rounding 
 These features made numerical computations more predictable and machine-independent, and made possible the efficient and consistent implementation of interval arithmetic.
Rounding 
 Most programming languages provide functions or special syntax to round fractional numbers in various ways.
Rounding 
 The earliest numeric languages, such as FORTRAN and C, would provide only one method, usually truncation (towards zero).
Rounding 
 This default method could be implied in certain contexts, such as when assigning a fractional number to an integer variable, or using a fractional number as an index of an array.
Rounding 
 Other kinds of rounding had to be programmed explicitly; for example, rounding a positive number to the nearest integer could be implemented by adding 0.5 and truncating.
Rounding 
 In the last decades, however, the syntax and/or the standard libraries of most languages have commonly provided at least the four basic rounding functions (up/ceiling, down/floor, to nearest, and towards zero).
Rounding 
 The tie-breaking method may vary depending the language and version, and/or may be selectable by the programmer.
Rounding 
 Several languages follow the lead of the IEEE-754 floating-point standard, and define these functions as taking a double precision float argument and returning the result of the same type, which then may be converted to an integer if necessary.
Rounding 
 Since the IEEE double precision format has 52 fraction bits, this approach may avoid spurious overflows in languages have 32-bit integers.
Rounding 
 Some languages, such as PHP, provide functions that round a value to a specified number of decimal digits, e.g. from 4321.5678 to 4321.57 or 4300.
Rounding 
 In addition, many languages provide a "printf" or similar string formatting function, which allows one to convert a fractional number to a string, rounded to a user-specified number of decimal places (the precision).
Rounding 
 On the other hand, truncation (round to zero) is still the default rounding method used by many languages, especially for the division of two integer values.
Rounding 
 On the opposite, CSS and SVG do not define any specific maximum precision for numbers and measurements, that are treated and exposed in their Document Object Model and in their Interface-description-language interface as strings as if they had infinite precision, and do not discriminate between integers and floating point values; however, the implementations of these languages will typically convert these numbers into IEEE-754 double floating points before exposing the computed digits with a limited precision (notably within standard Javascript or ECMAScript interface bindings).
Rounding 
 In a guideline issued in mid-1966, the U.S. Office of the Federal Coordinator for Meteorology determined that weather data should be rounded to the nearest  round number, with the "round half up" tie-breaking rule.
Rounding 
 Some meteorologists may write "-0" to indicate a temperature between 0.0 and -0.5 degrees (exclusive) that was rounded to integer.
Rounding 
 This notation is used when the negative sign is considered important, no matter how small is the magnitude; for example, when rounding temperatures in the Celsius scale, where below zero indicates freezing.
Rounding 
 An introduction to different rounding algorithms  that is accessible to a general audience but especially useful to those studying computer science and electronics.
Wheatland, Wyoming 
 Steamboat, the bucking horse on the license plate for the state of Wyoming and the logo for the athletics team of the University of Wyoming, was stabled in a barn in Wheatland.
Hitoshi Matsumoto 
 Hitoshi Matsumoto (born September 8, 1963 in Amagasaki Hyōgo) is an Japanese comedian, actor, producer and director.
Hitoshi Matsumoto 
 Matsumoto is probably best known for being one-half of the comedy duo, Downtown where he is the boke also with member Masatoshi Hamada who is the tsukkomi.
Hitoshi Matsumoto 
 While apart of Downtown, Matsumoto and Hamada made two television shows, Downtown no Gaki no Tsukai ya Arahende!!
Hitoshi Matsumoto 
 The movie was nominated in 2007 for "Best Film" at the Sitges - Catalonian International Film Festival and in 2008 for "Best Visual Effects" at the Asian Film Awards.
Kočevski Rog massacre 
 Thousands of members of the Slovene Home Guard and their families were executed by special units of the Yugoslav Partisans.
Kočevski Rog massacre 
 Several thousand (between 10,000 and 12,000, according to certain sources) war prisoners died in these executions.
Kočevski Rog massacre 
 The Russian British author Nikolai Tolstoy wrote an account of the events in his book The Minister and the Massacres.
Kočevski Rog massacre 
 British author John Corsellis, who served in Austria with the British Army, has written a historic book of these events, called Slovenia 1945: Memories of Death and Survival after World War II.
Kočevski Rog massacre 
 Boris Karapandzic writes that there were 12,000 Slovenian "home guards", 3,000 Serbian volunteer troops, 1,000 Montenegrin "chetniks", and 2,500 Croatian "home guards".
St Dennis, Cornwall 
 The area is full of tips and clay pits of china clay mining but St Dennis village itself is designated an 'island settlement' which prevents encroachment by the china clay industry.
St Dennis, Cornwall 
 Much of the parish is up to 500 feet above sea level, and the countryside is moorland with small fields enclosed by 'Cornish hedges'.
St Dennis, Cornwall 
 The tower is the oldest part of the church, and the newer church has been repaired after being destroyed by fire in 1985.
St Dennis, Cornwall 
 The village also has a strong history of Methodism and once had three Methodist chapels, two of these are still in use.
Illogan 
 Originally a rural area supporting itself by farming and agriculture, Illogan shared in the general prosperity brought about by the 19th century mining boom, which was experienced by the whole Camborne-Redruth area.
Illogan 
 St Illogan Church Parish stretching from Piece and Carnkie, to Portreath on the North Coast; Brea and Tuckingmill along the River Connor to the West; and Porthtowan, Sparnon Gate and Redruth Coombe to the East.
Illogan 
 Illogan Civil Parish stretching from Bridge and Harris Mill in the East; Tolvaddon and Bell Lake in the West; and from the A30 to Reskajeage on the North Cliffs.
Illogan 
 In 1985, civil parish status was given back to Illogan, but as the population was too large, Illogan was divided into the civil parishes of Carn Brea, Illogan and Portreath.
St Keverne 
 The leader of the rebellion Michael An Gof was a blacksmith from St Keverne and is commemorated by a statue in the village.
St Keverne 
 The parish is a large one and includes some 10 miles of coast from Nare Point at the mouth of the Helford River to Kennack Sands, and the Manacles offshore.
Cornish Rebellion of 1497 
 The Cornish Rebellion of 1497 was a popular uprising by the people of Cornwall in the far southwest of Britain.
Cornish Rebellion of 1497 
 Its primary cause was the people's response to the raising of war taxes by King Henry VII to pay for a campaign against Scotland.
Cornish Rebellion of 1497 
 Tin miners were angered as the scale of the taxes overturned previous rights granted by Edward I of England to the Cornish Stannary Parliament which exempted Cornwall from all taxes of 10ths or 15ths of income.
Cornish Rebellion of 1497 
 In reaction to King Henry's tax levy, Michael Joseph (An Gof), a blacksmith from St Keverne and Thomas Flamank a lawyer from Bodmin, persuaded many of the people of Cornwall to revolt against the King.
Cornish Rebellion of 1497 
 An army of 15,000 marched into Devon, attracting support in terms of provisions and recruits as they went.
Cornish Rebellion of 1497 
 Apart from one isolated incident at Taunton their march was not accompanied by any violence or looting.
Cornish Rebellion of 1497 
 From Taunton, they moved on to Wells, where they were joined by the seventh Baron Audley, an able soldier.
Cornish Rebellion of 1497 
 After issuing a declaration of grievances, the army left Wells and marched to Winchester via Bristol and Salisbury, remarkably unopposed as they progressed across the south of England.
Cornish Rebellion of 1497 
 At this point, having come so far, there seems to have been some questioning of what exactly should be done.
Cornish Rebellion of 1497 
 Flamank proposed that they should head for Kent, 'the classic soil of protests', the home of the Peasants' Revolt of 1381 and Jack Cade's rebellion, to rally the volatile men of Kent to their banner.
Cornish Rebellion of 1497 
 Having failed to attract support in Kent part of the army abandoned the march and returned home while the rest turned towards Surrey.
Cornish Rebellion of 1497 
 The same day that the Cornish arrived at Guildford, Lord Daubeney and his army took up position upon Hounslow Heath and were cheered by the arrival of food and wine dispatched by the Lord Mayor of London.
Cornish Rebellion of 1497 
 Lord Daubeney sent out a force of 500 mounted spearmen and they clashed with the Cornish at 'Gill Down' outside Guildford on Wednesday 14 June 1497.
Cornish Rebellion of 1497 
 The Cornish army left Guildford and moved via Banstead and Chussex Plain to Blackheath where they pitched their final camp, looking down from the hill onto the Thames and City of London.
Cornish Rebellion of 1497 
 Somehow An Gof held his army together, but faced with overwhelming odds, some Cornish deserted and by morning there remained only some 9-10,000 Cornish stalwarts left in arms.