NaN

In computing, NaN, standing for not a number, is a numeric data type value representing an undefined or unrepresentable value, especially in floating-point arithmetic. Systematic use of NaNs was introduced by the IEEE 754 floating-point standard in 1985, along with the representation of other non-finite quantities such as infinities.

For example, 0/0 is undefined as a real number, and is therefore represented by NaN. The square root of a negative number is an imaginary number and cannot be represented as a real number, so is represented by NaN. NaNs may also be used to represent missing values in computations.[1][2]

Two separate kinds of NaNs are provided, termed quiet NaNs and signaling NaNs. Quiet NaNs are used to propagate errors resulting from invalid operations or values. Signaling NaNs can support advanced features such as mixing numerical and symbolic computation or other extensions to basic floating-point arithmetic.

Floating point

In floating-point calculations, NaN is not the same as infinity, although both are typically handled as special cases in floating-point representations of real numbers as well as in floating-point operations. An invalid operation is also not the same as an arithmetic overflow (which might return an infinity) or an arithmetic underflow (which would return the smallest normal number, a denormal number, or zero).

IEEE 754 NaNs are represented with the exponent field filled with ones (like infinity values), and some non-zero number in the significand (to make them distinct from infinity values); this representation allows the definition of multiple distinct NaN values, depending on which bits are set in the significand, but also on the value of the leading sign bit (but applications are not required to provide distinct semantics for those distinct NaN values).

For example, a bit-wise IEEE floating-point standard single precision (32-bit) NaN would be: s111 1111 1xxx xxxx xxxx xxxx xxxx xxxx where s is the sign (most often ignored in applications) and the x sequence represents a non-zero number (the value zero encodes infinities). The first bit from x is used to determine the type of NaN: "quiet NaN" or "signaling NaN". The remaining bits encode a payload (most often ignored in applications).

Floating-point operations other than ordered comparisons normally propagate a quiet NaN (qNaN). Most floating-point operations on a signaling NaN (sNaN) signal the invalid operation exception, the default exception action is then the same as for qNaN operands and they produce a qNaN if producing a floating-point result.

The propagation of quiet NaNs through arithmetic operations allows errors to be detected at the end of a sequence of operations without extensive testing during intermediate stages. For example, if one starts with a NaN and adds 1 five times in a row, each addition results in a NaN, but there is no need to check each calculation because one can just note that the final result is NaN. However, depending on the language and the function, NaNs can silently be removed from a chain of calculations where one calculation in the chain would give a constant result for all other floating-point values. For example, the calculation x^0, may produce the result 1, even where x is NaN, so checking only the final result would obscure the fact that a calculation before the x^0 resulted in NaN. In general, then, a later test for a set invalid flag is needed to detect all cases where NaNs are introduced [3] (see Function definition below for further details).

In section 6.2 of the current IEEE 754-2008 standard there are two anomalous functions (the maxnum and minnum functions that return the maximum of two operands that are expected to be numbers) that favor numbers — if just one of the operands is a NaN then the value of the other operand is returned. For the next revision of the IEEE 754 standard, it is planned to replace these functions as they are not associative (when a signaling NaN appears in an operand).[4]

Comparison with NaN

A comparison with a NaN always returns an unordered result even when comparing with itself. The comparison predicates are either signaling or non-signaling on quiet NaN operands; the signaling versions signal the invalid operation exception for such comparisons. The equality and inequality predicates are non-signaling so x = x returning false can be used to test if x is a quiet NaN. The other standard comparison predicates are all signaling if they receive a NaN operand, the standard also provides non-signaling versions of these other predicates. The predicate isNaN(x) determines if a value is a NaN and never signals an exception, even if x is a signaling NaN.

Operations generating NaN

There are three kinds of operations that can return NaN:[5]

  • Most operations with a NaN as at least one operand.
  • Indeterminate forms:
    • The divisions (±0) / (±0) and (±∞) / (±∞).
    • The multiplications (±0) × (±∞) and (±∞) × (±0).
    • Remainder x % y when x is an infinity or y is zero.
    • The additions (+∞) + (−∞), (−∞) + (+∞) and equivalent subtractions (+∞) − (+∞) and (−∞) − (−∞).
    • The standard has alternative functions for powers:
      • The standard pow function and the integer exponent pown function define 0⁰, 1, and ∞⁰ as 1.
      • The powr function defines all three indeterminate forms as invalid operations and so returns NaN.
  • Real operations with complex results, for example:
    • The square root of a negative number.
    • The logarithm of a negative number.
    • The inverse sine or cosine of a number that is less than −1 or greater than 1.

NaNs may also be explicitly assigned to variables, typically as a representation for missing values. Prior to the IEEE standard, programmers often used a special value (such as −99999999) to represent undefined or missing values, but there was no guarantee that they would be handled consistently or correctly.[1]

NaNs are not necessarily generated in all the above cases. If an operation can produce an exception condition and traps are not masked then the operation will cause a trap instead.[6] If an operand is a quiet NaN, and there isn't also a signaling NaN operand, then there is no exception condition and the result is a quiet NaN. Explicit assignments will not cause an exception even for signaling NaNs.

Quiet NaN

Quiet NaNs, or qNaNs, do not raise any additional exceptions as they propagate through most operations. The exceptions are where the NaN cannot simply be passed through unchanged to the output, such as in format conversions or certain comparison operations (which do not "expect" a NaN input).

Signaling NaN

Signaling NaNs, or sNaNs, are special forms of a NaN that when consumed by most operations should raise the invalid operation exception and then, if appropriate, be "quieted" into a qNaN that may then propagate. They were introduced in IEEE 754. There have been several ideas for how these might be used:

  • Filling uninitialized memory with signaling NaNs would produce the invalid operation exception if the data is used before it is initialized
  • Using an sNaN as a placeholder for a more complicated object, such as:

When encountered, a trap handler could decode the sNaN and return an index to the computed result. In practice, this approach is faced with many complications. The treatment of the sign bit of NaNs for some simple operations (such as absolute value) is different from that for arithmetic operations. Traps are not required by the standard. There are other approaches to this sort of problem that would be more portable.

Function definition

There are differences of opinion about the proper definition for the result of a numeric function that receives a quiet NaN as input. One view is that the NaN should propagate to the output of the function in all cases to propagate the indication of an error. Another view, and the one taken by the ISO C99 and IEEE 754-2008 standards in general, is that if the function has multiple arguments and the output is uniquely determined by all the non-NaN inputs (including infinity), then that value should be the result. Thus for example the value returned by hypot(±∞,qNaN) and hypot(qNaN,±∞) is +∞.

The problem is particularly acute for the exponentiation function pow(x,y) = xy. The expressions 00, ∞0 and 1 are considered indeterminate forms when they occur as limits (just like ∞ × 0), and the question of whether zero to the zero power should be defined as 1 has divided opinion.

If the output is considered as undefined when a parameter is undefined, then pow(1,qNaN) should produce a qNaN. However, math libraries have typically returned 1 for pow(1,y) for any real number y, and even when y is an infinity. Similarly, they produce 1 for pow(x,0) even when x is 0 or an infinity. The rationale for returning the value 1 for the indeterminate forms was that the value of functions at singular points can be taken as a particular value if that value is in the limit the value for all but a vanishingly small part of a ball around the limit value of the parameters. The 2008 version of the IEEE 754 standard says that pow(1,qNaN) and pow(qNaN,0) should both return 1 since they return 1 whatever else is used instead of quiet NaN. Moreover, ISO C99, and later IEEE 754-2008, chose to specify pow(−1,±∞) = 1 instead of qNaN; the reason of this choice is given in the C rationale:[7] "Generally, C99 eschews a NaN result where a numerical value is useful. [...] The result of pow(−2,∞) is +∞, because all large positive floating-point values are even integers."

To satisfy those wishing a more strict interpretation of how the power function should act, the 2008 standard defines two additional power functions: pown(x,n), where the exponent must be an integer, and powr(x,y), which returns a NaN whenever a parameter is a NaN or the exponentiation would give an indeterminate form.

Integer NaN

Most fixed-size integer formats do not have any way of explicitly indicating invalid data. Converting NaN to an integer type, or performing an integer operation whose floating-point equivalent would produce NaN, usually throws an exception. In Java, such operations throw instances of java.lang.ArithmeticException.[8] In C, they lead to undefined behavior.

Perl's Math::BigInt package uses "NaN" for the result of strings that don't represent valid integers.[9]

> perl -mMath::BigInt -e "print Math::BigInt->new('foo')"
NaN

Display

Different operating systems and programming languages may have different string representations of NaN.

 nan
 NaN
 NaN%
 NAN
 NaNQ
 NaNS
 qNaN
 sNaN
 1.#SNAN
 1.#QNAN
 -1.#IND

Since, in practice, encoded NaNs have a sign, a quiet/signaling bit and optional 'diagnostic information' (sometimes called a payload), these will often be found in string representations of NaNs, too, for example:

 -NaN
  NaN12345
 -sNaN12300
 -NaN(s1234)

(other variants exist).

Encoding

In IEEE 754 standard-conforming floating-point storage formats, NaNs are identified by specific, pre-defined bit patterns unique to NaNs. The sign bit does not matter. Binary format NaNs are represented with the exponential field filled with ones (like infinity values), and some non-zero number in the significand field (to make them distinct from infinity values). The original IEEE 754 standard from 1985 (IEEE 754-1985) only described binary floating-point formats, and did not specify how the signaling/quiet state was to be tagged. In practice, the most significant bit of the significand field determined whether a NaN is signaling or quiet. Two different implementations, with reversed meanings, resulted:

  • most processors (including those of the Intel and AMD's x86 family, the Motorola 68000 family, the AIM PowerPC family, the ARM family, the Sun SPARC family, and optionally new MIPS processors) set the signaling/quiet bit to non-zero if the NaN is quiet, and to zero if the NaN is signaling. Thus, on these processors, the bit represents an 'is_quiet' flag;
  • in NaNs generated by the PA-RISC and old MIPS processors, the signaling/quiet bit is zero if the NaN is quiet, and non-zero if the NaN is signaling. Thus, on these processors, the bit represents an 'is_signaling' flag.

The former choice has been preferred as it allows the implementation to quiet a signaling NaN by just setting the signaling/quiet bit to 1. The reverse is not possible with the latter choice because setting the signaling/quiet bit to 0 could yield an infinity.

The 2008 revision of the IEEE 754 standard (IEEE 754-2008) makes formal recommendations for the encoding of the signaling/quiet state.

  • For binary formats, the most significant bit of the significand field should be an 'is_quiet' flag. I.e. this bit is non-zero if the NaN is quiet, and zero if the NaN is signaling.
  • For decimal formats, whether binary or decimal encoded, a NaN is identified by having the top five bits of the combination field after the sign bit set to ones. The sixth bit of the field is the 'is_quiet' flag. The standard follows the interpretation as an 'is_signaling' flag. I.e. the signaling/quiet bit is zero if the NaN is quiet, and non-zero if the NaN is signaling. A signaling NaN is quieted by clearing this sixth bit.

For IEEE 754-2008 conformance, the meaning of the signaling/quiet bit in recent MIPS processors is now configurable via the NAN2008 field of the FCSR register. This support is optional in MIPS Release 3 and required in Release 5.[10]

The state/value of the remaining bits of the significand field are not defined by the standard. This value is called the 'payload' of the NaN. If an operation has a single NaN input and propagates it to the output, the result NaN's payload should be that of the input NaN (this is not always possible for binary formats when the signaling/quiet state is encoded by an 'is_signaling' flag, as explained above). If there are multiple NaN inputs, the result NaN's payload should be from one of the input NaNs; the standard does not specify which.

References

  1. ^ a b Bowman, Kenneth (2006). An Introduction to Programming with IDL: Interactive Data Language. Academic Press. p. 26. ISBN 978-0-12-088559-6.
  2. ^ Press, William H.; Teukolsky, Saul A.; Vetterling, William T.; Flannery, Brian P. (2007). Numerical Recipes: The Art of Scientific Computing. Cambridge University Press. p. 34. ISBN 978-0-521-88068-8.
  3. ^ William Kahan (1 October 1997). "Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic" (PDF).
  4. ^ "754R Minutes". 19 May 2017. Retrieved 25 June 2017.
  5. ^ David Goldberg. "What Every Computer Scientist Should Know About Floating-Point".
  6. ^ "Intel 64 and IA-32 Architectures Software Developer's Manual Volume 1: Basic Architecture". April 2008. pp. 118–125, 266–267, 334–335.
  7. ^ "Rationale for International Standard—Programming Languages—C, Revision 5.10" (PDF). April 2003. p. 180.
  8. ^ "ArithmeticException (Java Platform SE 8 )". docs.oracle.com.
  9. ^ "Math::BigInt". perldoc.perl.org. Retrieved 12 June 2015.
  10. ^ "MIPS® Architecture For Programmers – Volume I-A: Introduction to the MIPS64® Architecture" (PDF). MIPS Technologies, Inc. 20 November 2013. p. 79. Retrieved 27 September 2017.

External links

BBC Radio nan Gàidheal

BBC Radio nan Gàidheal is a Scottish radio station, broadcasting in Scottish Gaelic. It is operated by the BBC as part of its portfolio of television and radio services in Scotland.

The station is available from FM transmitters throughout Scotland: its service licence states that "BBC Radio nan Gàidheal should be available every day for general reception across Scotland on FM"; it can also be heard on digital television platforms, DAB Digital Radio, and online.

BBC Radio nan Gàidheal programmes are also broadcast (with an in-vision graphical overlay) on the Scottish Gaelic digital television channel BBC Alba during periods when the channel is not carrying television programmes.

Comhairle nan Eilean Siar

Comhairle nan Eilean Siar (Scottish Gaelic pronunciation: [ˈkʰõ.ərˠʎə nə ˈɲelan ˈʃiəɾ]) is the local government council for Na h-Eileanan Siar council area of Scotland, comprising the Outer Hebrides. It is based in Stornoway in the Isle of Lewis.

Henan

Henan (河南; formerly romanized as Honan), is a province of the People's Republic of China, located in the central part of the country. Henan is often referred to as Zhongyuan or Zhongzhou (中州) which literally means "central plain land" or "midland", although the name is also applied to the entirety of China proper. Henan is the birthplace of Chinese civilization with over 3,000 years of recorded history, and remained China's cultural, economical, and political center until approximately 1,000 years ago.

Henan province is a home to a large number of heritage sites which have been left behind including the ruins of Shang dynasty capital city Yin and the Shaolin Temple. Four of the Eight Great Ancient Capitals of China, Luoyang, Anyang, Kaifeng, and Zhengzhou are located in Henan. The practice of Tai Chi also began in Chen Jia Gou Village (Chen style), as did the later Yang and Wu styles.Although the name of the province (河南) means "south of the [Yellow] river", approximately a quarter of the province lies north of the Yellow River, also known as the Huang He. With an area of 167,000 km2 (64,479 sq mi), Henan covers a large part of the fertile and densely populated North China Plain. Its neighboring provinces are Shaanxi, Shanxi, Hebei, Shandong, Anhui, and Hubei. Henan is China's third most populous province with a population of over 94 million. If it were a country by itself, Henan would be the 14th most populous country in the world, ahead of Egypt and Vietnam.

Henan is the 5th largest provincial economy of China and the largest among inland provinces. However, per capita GDP is low compared to other eastern and central provinces.

Henan is considered to be one of the less developed areas in China. The economy continues to grow based on aluminum and coal prices, as well as agriculture, heavy industry, tourism, and retail. High-tech industries and service sector is underdeveloped and is concentrated around Zhengzhou and Luoyang.

Hoklo people

The Hoklo people are Han Chinese people whose traditional ancestral homes are in southern Fujian, China and speakers of Hokkien which is the prestige dialect of the Southern Min varieties. They are also known by various endonyms (Pe̍h-ōe-jī: Hok-ló-lâng/Hō-ló-lâng/Ho̍h-ló-lâng/Hô-ló-lâng), or other related terms such as Banlam (Minnan) people (閩南儂; Bân-lâm-lâng) or Hokkien people (福建儂; Hok-kiàn-lâng). "Hokkien" is sometimes erroneously used to refer to all Fujianese people.

"Hoklo people" of this page refers to people whose native language is the Quanzhang Minnan (Hokkien-Taiwanese) spoken in Southern Fujian (China's province), Taiwan, Malaysia, Singapore, Indonesia, the Philippines and by many overseas Chinese throughout Southeast Asia.

There have been many famous Hoklo people throughout history, notably Koxinga, Shi Lang, Corazon Aquino and Su Song.

Huainanzi

The Huainanzi is an ancient Chinese text that consists of a collection of essays that resulted from a series of scholarly debates held at the court of Liu An, Prince of Huainan, sometime before 139 BC. The Huainanzi blends Daoist, Confucianist, and Legalist concepts, including theories such as yin and yang and Wu Xing theories.

The Huainanzi's essays are all connected to one primary goal: attempting to define the necessary conditions for perfect socio-political order. It concludes that perfect societal order derives mainly from a perfect ruler, and the essays are compiled in such a way as to serve as a handbook for an enlightened sovereign and his court.

Hunan

Hunan (湖南) is a province of the People's Republic of China, located in the middle reaches of the Yangtze watershed in South Central China; it borders the province-level divisions of Hubei to the north, Jiangxi to the east, Guangdong and Guangxi to the south, Guizhou to the west, and Chongqing to the northwest. With a population of just over 67 million as of 2014 residing in an area of approximately 210,000 km2 (81,000 sq mi), it is China's 7th most populous and the 10th most extensive province-level by area.

The name Hunan literally means "south of the lake"; Hu means "lake" while nan means "south.". The lake that is referred to is Dongting Lake, a lake in the northeast of the province; Vehicle license plates from Hunan are marked Xiāng (Chinese: 湘), after the Xiang River, which runs from south to north through Hunan and forms part of the largest drainage system for the province. Its capital and largest city is Changsha, which also abuts the Xiang River.

Jiangnan

Jiangnan or Jiang Nan (Chinese: 江南; pinyin: Jiāngnán; Wu: Kaon平 noe去; formerly romanized Kiang-nan, literally "South of the river") is a geographic area in China referring to lands immediately to the south of the lower reaches of the Yangtze River, including the southern part of its delta. The region encompasses the city of Shanghai, the southern part of Jiangsu Province, the entire Zhejiang Province, the southeastern part of Anhui Province, the northern part of Jiangxi and Fujian Provinces. The most important cities in the area are Shanghai, Anqing, Changzhou, Hangzhou, Nanjing, Ningbo, Shaoxing, Suzhou, Wuxi, Zhenjiang and Fuzhou.

Jiangnan has long been regarded as one of the most prosperous regions in China due to its wealth in natural resources and very high human development. Most People of the region speak Jiangnan Mandarin and Wu Chinese dialects as their native languages.

Jinan

Jinan, formerly romanized as Tsinan, is the capital of Shandong province in Eastern China. The area of present-day Jinan has played an important role in the history of the region from the earliest beginnings of civilization and has evolved into a major national administrative, economic, and transportation hub. The city has held sub-provincial administrative status since 1994. Jinan is often called the "Spring City" for its famous 72 artesian springs.

Its population was 6.8 million at the 2010 census.

NAN-190

NAN-190 is a drug and research chemical widely used in scientific studies. It was previously believed to act as a selective 5-HT1A receptor antagonist, but a subsequent discovery showed that it also potently blocks the α2-adrenergic receptor. The new finding has raised significant concerns about studies using NAN-190 as a specific serotonin receptor antagonist.

Naan

Naan (Hindi: नान, translit. nān) is a leavened, oven-baked flatbread found in the cuisines mainly of West Asia, Central Asia, Southeast Asia, the Indian subcontinent and the Caribbean.

Nan-sous-Thil

Nan-sous-Thil is a commune in the Côte-d'Or department in eastern France.

Nan Huai-Chin

Nan Huai-Chin (simplified Chinese: 南怀瑾; traditional Chinese: 南懷瑾; pinyin: Nán Huáijǐn) (March 18, 1918 – September 29, 2012) was a spiritual teacher of contemporary China. He was considered by many to be the major force in the revival of Chinese Buddhism. While Nan was regarded by many in China as one of the most influential Chan Buddhist teachers, he was little known outside the Chinese cultural sphere. Nan died at the age of 95 on Sept. 29th, 2012 in Suzhou, China.

Nan Province

Nan (Thai: น่าน, pronounced [nâːn]) is one of the northern provinces (changwat) of Thailand. Neighboring provinces are (from south clockwise): Uttaradit, Phrae, and Phayao. To the north and east it borders Sainyabuli of Laos.

Nanjing

Nanjing (listen), formerly romanized as Nanking and Nankin, is the capital of Jiangsu province of the People's Republic of China and the second largest city in the East China region, with an administrative area of 6,600 km2 (2,500 sq mi) and a total population of 8,270,500 as of 2016. The inner area of Nanjing enclosed by the city wall is Nanjing City (南京城), with an area of 55 km2 (21 sq mi), while the Nanjing Metropolitan Region includes surrounding cities and areas, covering over 60,000 km2 (23,000 sq mi), with a population of over 30 million.

Situated in the Yangtze River Delta region, Nanjing has a prominent place in Chinese history and culture, having served as the capital of various Chinese dynasties, kingdoms and republican governments dating from the 3rd century to 1949, and has thus long been a major center of culture, education, research, politics, economy, transport networks and tourism, being the home to one of the world's largest inland ports. The city is also one of the fifteen sub-provincial cities in the People's Republic of China's administrative structure, enjoying jurisdictional and economic autonomy only slightly less than that of a province. Nanjing has been ranked seventh in the evaluation of "Cities with Strongest Comprehensive Strength" issued by the National Statistics Bureau, and second in the evaluation of cities with most sustainable development potential in the Yangtze River Delta. It has also been awarded the title of 2008 Habitat Scroll of Honor of China, Special UN Habitat Scroll of Honor Award and National Civilized City. Nanjing boasts many high-quality universities and research institutes, with the number of universities listed in 100 National Key Universities ranking third, including Nanjing University which has a long history and is among the world top 10 universities ranked by Nature Index. The ratio of college students to total population ranks No.1 among large cities nationwide. Nanjing is one of the top three Chinese scientific research centers, according to the Nature Index, especially strong in the chemical sciences.

Nanjing, one of the nation's most important cities for over a thousand years, is recognized as one of the Four Great Ancient Capitals of China. It has been one of the world's largest cities, enjoying peace and prosperity despite wars and disasters. Nanjing served as the capital of Eastern Wu (229–280), one of the three major states in the Three Kingdoms period; the Eastern Jin and each of the Southern dynasties (Liu Song, Southern Qi, Liang and Chen), which successively ruled southern China from 317–589; the Southern Tang (937–75), one of the Ten Kingdoms; the Ming dynasty when, for the first time, all of China was ruled from the city (1368–1421); and the Republic of China (1927–37, 1946–49) prior to its flight to Taiwan during the Chinese Civil War. The city also served as the seat of the rebel Taiping Heavenly Kingdom (1853–64) and the Japanese puppet regime of Wang Jingwei (1940–45) during the Second Sino-Japanese War. It suffered severe atrocities in both conflicts, including the Nanjing Massacre.

Nanjing has served as the capital city of Jiangsu province since the establishment of the People's Republic of China. It boasts many important heritage sites, including the Presidential Palace and Sun Yat-sen Mausoleum. Nanjing is famous for human historical landscapes, mountains and waters such as Fuzimiao, Ming Palace, Chaotian Palace, Porcelain Tower, Drum Tower, Stone City, City Wall, Qinhuai River, Xuanwu Lake and Purple Mountain. Key cultural facilities include Nanjing Library, Nanjing Museum and Nanjing Art Museum.

Nanning

Nanning (Chinese: 南宁; pinyin: Nánníng; Zhuang: Namzningz) is the capital and largest city by population of the Guangxi Zhuang Autonomous Region in southern China. It is known as the "Green City" because of its abundance of lush subtropical foliage. As of 2014 it had a population of 6,913,800 with 4,037,000 in its urban area.

South China Sea

The South China Sea is a marginal sea that is part of the Pacific Ocean, encompassing an area from the Karimata and Malacca Straits to the Strait of Taiwan of around 3,500,000 square kilometres (1,400,000 sq mi). The sea carries tremendous strategic importance; one-third of the world's shipping passes through it, carrying over $3 trillion in trade each year, it contains lucrative fisheries, which are crucial for the food security of millions in Southeast Asia. Huge oil and gas reserves are believed to lie beneath its seabed.According to International Hydrographic Organization (IHO) Limits of Oceans and Seas, 3rd edition (1953), it is located

south of China;

east of Vietnam;

west of the Philippines;

east of the Malay Peninsula and Sumatra, up to the Strait of Singapore in the western, and

north of the Bangka Belitung Islands and BorneoHowever, in its unapproved draft 4th edition (1986), IHO proposed the Natuna Sea, thus the South China Sea southern boundary was shifted northward, from north of the Bangka Belitung Islands to

north and northeast of Natuna Islands.The minute South China Sea Islands, collectively an archipelago, number in the hundreds. The sea and its mostly uninhabited islands are subject to competing claims of sovereignty by several countries. These claims are also reflected in the variety of names used for the islands and the sea.

Southern Min

Southern Min or Minnan (simplified Chinese: 闽南语; traditional Chinese: 閩南語), literally "Southern Fujian" while "Min" is short for "Fujian" and "Nan" is "South", also known as Hokkien-Taiwanese, is a branch of Min Chinese spoken in certain parts of south and eastern China including Fujian (especially the Minnan region), most of Taiwan (many citizens are descendents of settlers from Fujian), eastern Guangdong, Hainan, and southern Zhejiang. The Minnan dialects are also spoken by descendants of emigrants from these areas in diaspora, most notably the Philippines, Indonesia, Malaysia and Singapore. It is the largest Min Chinese branch and the most widely distributed Min Chinese subgroup.

In common parlance and in the narrower sense, Southern Min refers to the Quanzhang or Hokkien-Taiwanese variety of Southern Min originating from Southern Fujian in Mainland China. It is spoken mainly in Fujian, Taiwan, as well as certain parts of Southeast Asia. The Quanzhang variety is often called simply "Minnan Proper" (simplified Chinese: 闽南语; traditional Chinese: 閩南語). It is considered the mainstream Southern Min Chinese Language.

In the wider scope, Southern Min also includes other Min Chinese varieties that are linguistically related to Minnan proper (Quanzhang). Most variants of Southern Min have significant differences from the Quanzhang variety, some having limited mutual intelligibility with it, others almost none. Teochew, Longyan, and Zhenan may be said to have limited mutual intelligibility with Minnan Proper, sharing similar phonology and vocabulary to a small extent. On the other hand, variants such as Datian, Zhongshan, and Qiong-Lei have historical linguistic roots with Minnan Proper, but are significantly divergent from it in terms of phonology and vocabulary, and thus have almost no mutual intelligibility with the Quanzhang variety. Linguists tend to classify them as separate Min languages.

Southern Min is not mutually intelligible with other branches of Min Chinese nor other varieties of Chinese, such as Mandarin.

Tír na nÓg

In Irish mythology Tír na nÓg ([tʲiːɾˠ n̪ˠə ˈn̪ˠoːɡ]; "Land of the Young") or Tír na hÓige ("Land of Youth") is one of the names for the Celtic Otherworld, or perhaps for a part of it. Other Old Irish names for the Otherworld include Tír Tairngire ("Land of Promise/Promised Land"), Tír fo Thuinn ("Land under the Wave"), Mag Mell ("Plain of Delight/Delightful Plain"), Ildathach ("Multicoloured place"), and Emain Ablach (the Isle of Apple Trees). Similar myths in the northern Celtic cultures include these of Annwn, Fairyland, and Hy Brasil.

Tír na nÓg is depicted as a paradise and supernatural realm of everlasting youth, beauty, health, abundance and joy. They enjoy a life of eating, dancing and loving and they never have to deal with death or dying. Its inhabitants are the Tuatha Dé Danann, the gods of pre-Christian Ireland. In the echtrae (adventure) and immram (voyage) tales, various Irish mythical heroes visit Tír na nÓg after a voyage or an invitation from one of its residents. They reach it by entering ancient burial mounds or caves, or by going under water or across the sea. The mortals who visit the Otherworld are referred to as echtrai (adventures) and baili (visions, ecstasies). The path across the sea is called Mag Mell (Plain of Honey). It is the golden path made by the sun on the ocean. The god that rules this region is said to be the first ancestor of the human race and the god of the dead.

Yunnan

Yunnan (云南) is a province of the People's Republic of China. Located in Southwest China, the province spans approximately 394,000 square kilometres (152,000 sq mi) and has a population of 45.7 million (as of 2009). The capital of the province is Kunming, formerly also known as Yunnan. The province borders the Chinese provinces Guangxi, Guizhou, Sichuan, and the Tibet Autonomous Region, as well as the countries Vietnam, Laos, and Myanmar.

Yunnan is situated in a mountainous area, with high elevations in the northwest and low elevations in the southeast. Most of the population lives in the eastern part of the province. In the west, the altitude can vary from the mountain peaks to river valleys by as much as 3,000 metres (9,800 ft). Yunnan is rich in natural resources and has the largest diversity of plant life in China. Of the approximately 30,000 species of higher plants in China, Yunnan has perhaps 17,000 or more. Yunnan's reserves of aluminium, lead, zinc and tin are the largest in China, and there are also major reserves of copper and nickel.

The Han Empire first recorded diplomatic relations with the province at the end of the 2nd century BC. It became the seat of a Sino-Tibetan-speaking kingdom of Nanzhao in the 8th century AD. Nanzhao was multi-ethnic, but the elite most-likely spoke a northern dialect of Yi. The Mongols conquered the region in the 13th century, with local control exercised by warlords until the 1930s. From the Yuan dynasty onward, the area was part of a central-government sponsored population movement towards the southwestern frontier, with two major waves of migrants arriving from Han-majority areas in northern and southeast China. As with other parts of China's southwest, Japanese occupation in the north during World War II forced another migration of majority Han people into the region. These two waves of migration contributed to Yunnan being one of the most ethnically diverse provinces of China, with ethnic minorities accounting for about 34 percent of its total population. Major ethnic groups include Yi, Bai, Hani, Zhuang, Dai and Miao.

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